• Harmonic Analysis
• Partial Differential Equations
• Geometric Measure Theory
  
  

• arXiv: https://arxiv.org/a/martell_j_1
• Google Scholar: https://scholar.google.com/citations?user=_py4-18AAAAJ
• MathScinet MR Author ID: 671782
• ORCID: 0000-0001-6788-4769
• Scopus Author ID: 57191576481
• Web of Science Reserach ID: C-6937-2008

Weights, extrapolation and the theory of Rubio de Francia
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Operator Theory: Advances and Applications, 215. Birkhäuser/Springer Basel AG, Basel, 2011
ISBN: 978-3-0348-0071-6.

The regularity problem for uniformly elliptic operators in weighted spaces
L. Chen, J.M. Martell, and C. Prisuelos-Arribas
Potential Anal. (to appear)

Elliptic measures and Square function estimates on 1-sided chord-arc domains
M. Cao, J.M. Martell, and A. Olivo
J. Geom. Anal. 32 (2022), no. 3, 77. 34 páginas

Uniform rectifiability and elliptic operators satisfying a Carleson measure condition.
S. Hofmann, J.M. Martell, S. Mayboroda, T. Toro, and Z. Zhao
Geom. Funct. Anal. 31 (2021), no. 2, 325-401

End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
K. Li, J.M. Martell, H. Martikainen, S. Ombrosi, and E. Vuorinen
Trans. Amer. Math. Soc. 374 (2021), no. 1, 97-135

Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem
J. Azzam, S. Hofmann, J.M. Martell, M. Mourgoglou, and X. Tolsa
Invent. Math. 222 (2020), no. 3, 881-993

Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates
J. Cavero, S. Hofmann, J.M. Martell, and T. Toro
Trans. Amer. Math. Soc. 373 (2020), no. 11, 7901-7935

The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper half-space
J.J. Marín, J.M. Martell, and M. Mitrea
Potential Anal. 53 (2020), no.3, 947-976

Extrapolation for multilinear Muckenhoupt classes and applications
K. Li, J.M. Martell, and S. Ombrosi
Adv. Math. 373 (2020), 107286. 43 páginas

Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach
Á. Bényi, J.M. Martell, K. Moen, E. Stachura, and R.H. Torres
Math. Ann. 376 (2020), no. 1-2, 61-102

Conical square functions for degenerate elliptic operators
L. Chen, J.M. Martell, and C. Prisuelos-Arribas
Adv. Calc. Var. 13 (2020), no. 1, 75-113

A Fatou Theorem and Poisson's Integral Representation Formula for Elliptic Systems in the Upper Half-Space
J.J. Marín, J.M. Martell, D. Mitrea, I. Mitrea, and M. Mitrea
Topics in Clifford Analysis: Special Volume in Honor of Wolfgang Sprößig, 105-124, Trends Math. Birkhäuser, Cham, 2019

Fatou-Type Theorems and Boundary Value Problems for Elliptic Systems in the Upper Half-Space
J.M. Martell, D. Mitrea, I. Mitrea, and M. Mitrea
Algebra i Analiz 31 (2019), no. 2, 3-50
St. Petersburg Math. J. 31 (2020), no. 2, 189–222

Rectifiability, interior approximation and Harmonic Measure
M. Akman, S. Bortz, S. Hofmann, and J.M. Martell
Ark. Mat. 57 (2019), no. 1, 1-22

Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators
J. Cavero, S. Hofmann, and J.M. Martell
Trans. Amer. Math. Soc. 371 (2019), no. 4, 2797-2835

The BMO-Dirichlet problem for elliptic systems in the upper half-space and quantitative characterizations of VMO
J.M. Martell, D. Mitrea, I. Mitrea, and M. Mitrea
Anal. PDE. 12 (2019), no. 3, 605-720

Weighted Hardy spaces associated with elliptic operators. Part II: Characterizations of \(H^1_L(w)\)
J.M. Martell and C. Prisuelos-Arribas
Publ. Mat. 62 (2018), no. 2, 475-535

Limited range multilinear extrapolation with applications to the bilinear Hilbert transform
D. Cruz-Uribe and J.M. Martell
Math. Ann. 371 (2018), no. 1, 615-653

On the Kato problem and extensions for degenerate elliptic operators
D. Cruz-Uribe, J.M. Martell, and C. Rios
Anal. PDE. 11 (2018), no. 3, 609-660

On the \(L^p\)-Poisson semigroup associated with elliptic systems
J.M. Martell, D. Mitrea, I. Mitrea and M. Mitrea
Potential Anal. 47 (2017), no. 4, 401-445

\(A_\infty\) implies NTA for a class of variable coefficient elliptic operators
S. Hofmann, J.M. Martell, and T. Toro
J. Differential Equations 263 (2017), no. 10, 6147-6188

Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries
M. Akman, M. Badger, S. Hofmann, and J.M. Martell
Trans. Amer. Math. Soc. 369 (2017), no. 8, 5711-5745

The weak-\(A_\infty\) property of harmonic and \(p\)-harmonic measures implies uniform rectifiability
S. Hofmann, P. Le, J.M. Martell, and K. Nyström
Anal. PDE. 10 (2017), no. 3, 513-558

Weighted Hardy spaces associated with elliptic operators. Part I: Weighted norm inequalities for conical square functions
C. Prisuelos-Arribas and J.M. Martell
Trans. Amer. Math. Soc. 369 (2017), no. 6, 4193-4233

A new characterization of chord-arc domains
J. Azzam, S. Hofmann, J.M. Martell, K. Nyström, and T. Toro
J. Eur. Math. Soc. (JEMS) 19 (2017), no. 4, 967-981

A note on the off-diagonal Muckenhoupt-Wheeden conjecture
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Advanced courses of mathematical analysis V, 244-252, World Sci. Publ. Hackensack, NJ, 2016.

The Dirichlet problem for elliptic systems with data in Köthe function spaces
J.M. Martell, D. Mitrea, I. Mitrea and M. Mitrea
Rev. Mat. Iberoam. 32 (2016), no. 3, 913-970

Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions
S. Hofmann, J.M. Martell, and S. Mayboroda
Duke Math. J. 165 (2016), no. 12, 2331-2389

Rectifiability of harmonic measure
J. Azzam, S. Hofmann, J.M. Martell, S. Mayboroda, M. Mourgoglou, X. Tolsa, and A. Volberg
Geom. Funct. Anal. 26 (2016), no. 3, 703-728

Oscillation estimates, self-improving results and good-\(\lambda\) inequalities
L. Berkovits, J. Kinnunen, and J.M. Martell
J. Funct. Anal. 270 (2016), no. 9, 3559-3590

Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure
J. Azzam, S. Hofmann, J.M. Martell, S. Mayboroda, M. Mourgoglou, X. Tolsa, and A. Volberg
C. R. Math. Acad. Sci. Paris. 354 (2016), 351-355

Greedy Bases in variable Lebesgue spaces
D. Cruz-Uribe, E. Hernández, and J.M. Martell
Monatsh. Math. 179 (2016), no. 3, 355-378

Self-improving properties for abstract Poincaré type inequalities
F. Bernicot and J.M. Martell
Trans. Amer. Math. 367, no. 7, (2015), 4793-4835

Dyadic harmonic analysis beyond doubling measures
L.D. López-Sánchez, J.M. Martell, and J. Parcet
Adv. Math. 267 (2014), 44-93

Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in \(L^p\)
S. Hofmann and J.M. Martell
Ann. Sci. École Norm. Sup. 47 (2014), no. 3, 577-654

Uniform rectifiability and harmonic measure II: Poisson kernels in \(L^p\) imply uniform rectifiability
S. Hofmann, J.M. Martell, and I. Uriarte-Tuero
Duke Math. J. 163 (2014), no. 8, 1601-1654

Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains
S. Hofmann, J.M. Martell, and S. Mayboroda
Int. Math. Res. Not. 2014 (2014), no. 10, 2702-2729

The higher order regularity Dirichlet problem for elliptic systems in the upper-half space
J.M. Martell, D. Mitrea, I. Mitrea and M. Mitrea
Harmonic Analysis and Partial Differential Equations
Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 11-15, 2012
Contemporary Mathematics 612 (2014), 123-141

Calderón-Zygmund operators associated to matrix-valued kernels
G. Hong, L.D. López-Sánchez, J.M. Martell, and J. Parcet
Int. Math. Res. Not. 2014 (2014), no. 5, 1221-1252

Self-improvement of Poincaré type inequalities associated with approximations of the identity and semigroups
A. Jiménez-del-Toro and J.M. Martell
Potential Anal. 38 (2013), no. 3, 805-841

Weighted norm inequalities on graphs
N. Badr and J.M. Martell
J. Geom. Anal. 22 (2012), no. 4, 1173-1210

Vertical versus conical square functions
P. Auscher, S. Hofmann, and J.M. Martell
Trans. Amer. Math. Soc. 364 (2012), no. 10, 5469-5489

Sharp weighted estimates for classical operators
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Adv. Math. 229 (2012), no. 1, 408-441

\(A_\infty\) estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators
S. Hofmann and J.M. Martell
Trans. Amer. Math. Soc. 364 (2012), no. 1, 65-101

\(L^p\) self-improvement of generalized Poincaré inequalities in spaces of homogeneous type
N. Badr, A. Jiménez-del-Toro, and J.M. Martell
J. Funct. Anal. 260 (2011), no. 11, 3147-3188

Quantifying democracy of wavelet bases in Lorentz spaces
E. Hernández, J.M. Martell, and M. de Natividade
Constr. Approx. 33 (2011), no. 1, 1-14

A note on \(A_\infty\) estimates via extrapolation of Carleson measures
S. Hofmann and J.M. Martell
The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis, ANU, Canberra, 13-17 July, 2009
Proceedings of the Centre for Mathematics and its Applications 44 (2010), 143-166

Sharp weighted estimates for approximating dyadic operators
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Electron. Res. Announc. Math. Sci. 17 (2010), 12-19

Weighted norm inequalities, off-diagonal estimates and elliptic operators
P. Auscher and J.M. Martell
Harmonic Analysis and Partial Differential Equations
Proceedings of the 8th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 16-20, 2008
Contemporary Mathematics 505 (2010), 61-83

Generalized Hörmander's conditions and weighted endpoint estimates
M. Lorente, J.M. Martell, C. Pérez, and M.S. Riveros
Studia Math. 195 (2009), no. 2, 157-192

Multilinear Extrapolation and applications to the bilinear Hilbert transform
M.J. Carro, L. Grafakos, J.M. Martell, and F. Soria
J. Math. Anal. Appl. 357 (2009), no. 2, 479-497

Weighted norm inequalities for fractional operators
P. Auscher and J.M. Martell),
Indiana Univ. Math. J. 57 (2008), no. 4, 1845-1870

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights
P. Auscher and J.M. Martell
Math. Z. 260 (2008), no. 3, 527-539

Generalized Hörmander's conditions, commutators and weights,
M. Lorente, J.M. Martell, M.S. Riveros, and A. de la Torre
J. Math. Anal. Appl. 342 (2008), no. 2, 1399-1425

Wavelets, Orlicz spaces, and greedy bases
G. Garrigós, E. Hernández, and J.M. Martell
Appl. Comput. Harmon. Anal. 24 (2008), no. 1, 70-93

Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Adv. Math. 216 (2007), no. 2, 647-676

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous type
P. Auscher and J.M. Martell
J. Evol. Equ. 7 (2007), 265-316

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights,
P. Auscher and J.M. Martell
Adv. Math. 212 (2007), no. 1, 225-276

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic Analysis of elliptic operators,
P. Auscher and J.M. Martell
J. Funct. Anal. 241 (2006), 703-746

Extrapolation with weights, Rearrangement Invariant Function Spaces, Modular inequalities and applications to Singular Integrals,
G.P. Curbera, J. García-Cuerva, J.M. Martell, and C. Pérez
Adv. Math. 203 (2006), no. 1, 256-318

The boundedness of classical operators on variable \(L^p\) spaces,
D. Cruz-Uribe, A. Fiorenza, J.M. Martell, and C. Pérez
Ann. Acad. Sci. Fenn. Math. 31 (2006), 239-264

Extensions of Rubio de Francia's extrapolation theorem
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial 2004)
Collect. Math. 2006, 195-231

Weighted weak-type inequalities and a conjecture of Sawyer
D. Cruz-Uribe, J.M. Martell, and C. Pérez
Int. Math. Res. Not. 30 (2005), no. 5, 1849-1871

Weighted norm inequalities for maximally modulated operators
L. Grafakos, J.M. Martell, and F. Soria
Math. Ann. 331 (2005), no. 2, 359-394

Lack of natural weighted estimates for some singular integral operators
J.M. Martell, C. Pérez, and R.Trujillo-González
Trans. Amer. Math. Soc. 357 (2005), no. 1, 385-396

Weighted norm inequalities for singular integral operators
J.M. Martell
Seminar of Mathematical Analysis (Malaga/Seville, 2003/2004), 119-129, Colecc. Abierta 71, Univ. Sevilla Secr. Publ., Seville, 2004

Weighted norm inequalities and extrapolation
J.M. Martell
Seminar of Mathematical Analysis (Malaga/Seville, 2003/2004), 131-149, Colecc. Abierta 71, Univ. Sevilla Secr. Publ., Seville, 2004

Extrapolation from \(A_\infty\) weights and applications
D. Cruz-Uribe, J.M. Martell, and C. Pérez
J. Funct. Anal. 213 (2004), 412-439

Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type
J.M. Martell
J. Math. Anal. Appl. 294 (2004), no. 1, 223-236

Extrapolation of weighted norm inequalities for multivariable operators and applications
L. Grafakos and J.M. Martell
J. Geom. Anal.14 (2004), no. 1, 19-46

Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications
J.M. Martell
Studia Math.161 (2004), 113-145

\(L^p\) bounds for Riesz Transforms and Square Roots Associated to Second Order Elliptic Operators
S. Hofmann and J.M. Martell
Publ. Mat. 47 (2003), no. 2, 497-515

Wavelet characterization of weighted spaces
J. García-Cuerva and J.M. Martell
J. Geom. Anal. 11 (2001), no. 2, 241-264

Two-weight norm inequalities for maximal operator and fractional integrals on non-homogeneous spaces
J. García-Cuerva and J.M. Martell
Indiana Univ. Math. J. 50 (2001), no. 3, 1241-1280

On the existence of principal values for the Cauchy integral on weighted Lebesgue spaces for non-doubling measures
J. García-Cuerva and J.M. Martell
J. Fourier Anal. Appl. 7 (2001), no. 5, 469-487

Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces
J. García-Cuerva and J.M. Martell
Publ. Mat. 44 (2000), no. 2, 613-640

Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
M. Akman, S. Hofmann, J.M. Martell, and T. Toro
arXiv:1901.08261v3

Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains
S. Hofmann, J.M. Martell, and S. Mayboroda
arXiv:1904.13116

On the \(A_\infty\) condition for elliptic operators in 1-sided NTA domains satisfying the capacity density condition.
M. Cao, Ó. Domínguez, J.M. Martell, and P. Tradacete
arXiv:2101.06064

Extrapolation on function and modular spaces, and applications.
M. Cao, J.J. Marín, and J.M. Martell
arXiv:2101.06253

Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
M. Akman, S. Hofmann, J.M. Martell, and T. Toro
arXiv:2103.10046

The regularity problem for degenerate elliptic operators in weighted spaces
P. Auscher, L. Chen, J.M. Martell, and C. Prisuelos-Arribas
arXiv:2106.14422

Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in \(L^p\) implies uniform rectifiability
S. Hofmann and J.M. Martell
arXiv:1505.06499

Absolute continuity between the surface measure and harmonic measure implies rectifiability
S. Hofmann, J.M. Martell, S. Mayboroda, X. Tolsa, and A. Volberg
arXiv:1507.04409

A sufficient geometric criterion for quantitative absolute continuity of harmonic measure
S. Hofmann and J.M. Martell
arXiv:1712.03696v1

Harmonic measure and quantitative connectivity: geometric characterization of the \(L^p\)-solvability of the Dirichlet problem. Part I
S. Hofmann and J.M. Martell
arXiv:1712.03696v3

Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case
S. Hofmann, J.M. Martell, S. Mayboroda, T. Toro, and Z. Zhao
arXiv:1710.06157

Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case
S. Hofmann, J.M. Martell, S. Mayboroda, T. Toro, and Z. Zhao
arXiv:1908.03161

Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
M. Akman, S. Hofmann, J.M. Martell, and T. Toro
arXiv:1901.08261v2