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Abstract:

We present dimension-free reverse Hölder inequalities for strong Ap∗ weights, 1 ≤ p< ∞. We also provide a proof for the full range of local integrability of A1∗ weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For p= ∞, we also provide a reverse Hölder inequality for certain product measures. As a corollary we derive mixed Ap∗-A∞∗ weighted estimates. © 2016, Mathematica Josephina, Inc.

Registro:

Documento: Artículo
Título:Reverse Hölder Property for Strong Weights and General Measures
Autor:Luque, T.; Pérez, C.; Rela, E.
Filiación:Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, C/ Nicolás Cabrera, 13-15, Madrid, 28049, Spain
Department of Mathematics, University of the Basque Country, Ikerbasque and BCAM, Bilbao, 48080, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Maximal functions; Muckenhoupt weights; Multiparameter harmonic analysis; Reverse Hölder inequality
Año:2017
Volumen:27
Número:1
Página de inicio:162
Página de fin:182
DOI: http://dx.doi.org/10.1007/s12220-016-9678-y
Título revista:Journal of Geometric Analysis
Título revista abreviado:J Geom Anal
ISSN:10506926
CODEN:JGANE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10506926_v27_n1_p162_Luque

Referencias:

  • Aalto, D., Berkovits, L., Asymptotical stability of Muckenhoupt weights through Gurov-Reshetnyak classes (2012) Trans. Am. Math. Soc., 364 (12), pp. 6671-6687
  • Agarwal, R.P., Ding, S., Nolder, C., (2009) Inequalities for differential forms, , Springer, New York
  • Astala, K., Iwaniec, T., Martin, G., (2009) Elliptic partial differential equations and quasiconformal mappings in the plane volume 48 of Princeton Mathematical, , 48, Princeton University Press, Princeton
  • Bojarski, B., Sbordone, C., Wik, I., The Muckenhoupt class A 1 (R) (1992) Stud. Math., 101 (2), pp. 155-163
  • Buckley, S.M., Estimates for operator norms on weighted spaces and reverse Jensen inequalities (1993) Trans. Am. Math. Soc., 340 (1), pp. 253-272
  • Chung, D., Cristina Pereyra, M., Perez, C., Sharp bounds for general commutators on weighted Lebesgue spaces (2012) Trans. Am. Math. Soc., 364 (3), pp. 1163-1177
  • Coifman, R.R., Fefferman, C., Weighted norm inequalities for maximal functions and singular integrals (1974) Stud. Math., 51, pp. 241-250
  • de Guzmán, M.: Differentiation of integrals in R n . With appendices by Antonio Córdoba, and Robert Fefferman, and two by Roberto Moriyón, Lecture Notes in Mathematics, Vol. 481. Springer, Berlin (1975); Duoandikoetxea, J., Martín-Reyes, F., Ombrosi, S.: On the A ∞ conditions for general bases. Math. Z. (2015); Fujii, N.: Weighted bounded mean oscillation and singular integrals. Math. Japon. 22(5):529–534, (1977/78); García-Cuerva, J., Francia, J.L.R., (1985) Weighted norm inequalities and related topics, , North-Holland Mathematics Studies, 116, North-Holland Publishing Co., Amsterdam
  • Gehring, F.W., The L p -integrability of the partial derivatives of a quasiconformal mapping (1973) Acta Math., 130, pp. 265-277
  • Hagelstein, P., Luque, T., Parissis, I., Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases (2015) Trans. Am. Math. Soc., 367 (11), pp. 7999-8032
  • Weighted Solyanik estimates for the strong maximal function (2015) Preprint, arXiv, 1410, p. 3402. , arXiv:1410.3402
  • Hruščev, S.V., A description of weights satisfying the A ∞ condition of Muckenhoupt (1984) Proc. Am. Math. Soc., 90 (2), pp. 253-257
  • Hytönen, T., Pérez, C., Sharp weighted bounds involving A ∞ (2013) Anal. PDE, 6 (4), pp. 777-818
  • Hytönen, T., Pérez, C., Rela, E., Sharp Reverse Hölder property for A ∞ weights on spaces of homogeneous type (2012) J. Funct. Anal., 263 (12), pp. 3883-3899
  • Iwaniec, T., Martin, G., (2001) Geometric function theory and non-linear analysis. Oxford Mathematical Monographs. The Clarendon Press, , Oxford University Press, New York
  • Kinnunen, J., Sharp results on reverse Hölder inequalities (1994) Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes, (95), p. 34
  • Kinnunen, J., A stability result on Muckenhoupt’s weights (1998) Publ. Math., 42 (1), pp. 153-163
  • Korenovskyy, A.A., Lerner, A.K., Stokolos, A.M., On a multidimensional form of F. Riesz’s, “rising sun” lemma (2005) Proc. Am. Math. Soc., 133 (5), pp. 1437-1440
  • Kurtz, D.S., Littlewood-Paley and multiplier theorems on weighted L p spaces (1980) Trans. Am. Math. Soc., 259 (1), pp. 235-254
  • Lerner, A.K., Ombrosi, S., An extrapolation theorem with applications to weighted estimates for singular integrals (2012) J. Funct. Anal., 262 (10), pp. 4475-4487
  • Lerner, AK.: Sheldy Ombrosi, and Carlos Pérez. Sharp A 1 bounds for Calderón–Zygmund operators and the relationship with a problem of Muckenhoupt and Wheeden. Int. Math. Res. Not. IMRN, (6):Art. ID rnm161, 11 (2008); Lerner, A.K., Ombrosi, S., Pérez, C., Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden (2009) J. Fourier Anal. Appl., 15 (3), pp. 394-403
  • Luque, Teresa, Parissis Ioannis: Sharp weighted norm inequalities for multiparameter operators. (preprint); Malaksiano, N.A., On exact inclusions of Gehring classes in Muckenhoupt classes (2001) Mat. Zametki, 70 (5), pp. 742-750
  • Nikolay Aleksandrovich Malaksiano, The precise embeddings of one-dimensional Muckenhoupt classes in Gehring classes (2002) Acta Sci. Math. (Szeged), 68 (1-2), pp. 237-248
  • Mateu, J., Mattila, P., Nicolau, A., Orobitg, J., BMO for nondoubling measures (2000) Duke Math. J., 102 (3), pp. 533-565
  • Melas, A.D., A sharp L p inequality for dyadic A 1 weights in R n (2005) Bull. Lond. Math. Soc., 37 (6), pp. 919-926
  • Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function (1972) Trans. Am. Math. Soc., 165, pp. 207-226
  • Orobitg, J., Pérez, C.: A p weights for nondoubling measures in R n and applications. Trans. Amer. Math. Soc. 354(5):2013–2033 (electronic) (2002); Pérez, C., Rela, E., A new quantitative two weight theorem for the Hardy-Littlewood maximal operator (2015) Proc. Am. Math. Soc., 143, pp. 641-655
  • Sjögren, P., A remark on the maximal function for measures in R n (1983) Am. J. Math., 105 (5), pp. 1231-1233
  • Sjögren, P., Soria, F., Sharp estimates for the non-centered maximal operator associated to Gaussian and other radial measures (2004) Adv. Math., 181 (2), pp. 251-275

Citas:

---------- APA ----------
Luque, T., Pérez, C. & Rela, E. (2017) . Reverse Hölder Property for Strong Weights and General Measures. Journal of Geometric Analysis, 27(1), 162-182.
http://dx.doi.org/10.1007/s12220-016-9678-y
---------- CHICAGO ----------
Luque, T., Pérez, C., Rela, E. "Reverse Hölder Property for Strong Weights and General Measures" . Journal of Geometric Analysis 27, no. 1 (2017) : 162-182.
http://dx.doi.org/10.1007/s12220-016-9678-y
---------- MLA ----------
Luque, T., Pérez, C., Rela, E. "Reverse Hölder Property for Strong Weights and General Measures" . Journal of Geometric Analysis, vol. 27, no. 1, 2017, pp. 162-182.
http://dx.doi.org/10.1007/s12220-016-9678-y
---------- VANCOUVER ----------
Luque, T., Pérez, C., Rela, E. Reverse Hölder Property for Strong Weights and General Measures. J Geom Anal. 2017;27(1):162-182.
http://dx.doi.org/10.1007/s12220-016-9678-y