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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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Volume 12, Issue 4

Issues

Volume 13 (2015)

Weighted inequalities for some integral operators with rough kernels

María Riveros
  • FaMAF, Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende y Haya de la Torre, s/n, Ciudad Universitaria, 5000, Córdoba, Argentina
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/ Marta Urciuolo
  • FaMAF, Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende y Haya de la Torre, s/n, Ciudad Universitaria, 5000, Córdoba, Argentina
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Published Online: 2014-01-17 | DOI: https://doi.org/10.2478/s11533-013-0362-1

Abstract

In this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

MSC: 42B20; 42B25

Keywords: Fractional operators; Calderón-Zygmund operators; BMO; Muckenhoupt weights

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About the article

Published Online: 2014-01-17

Published in Print: 2014-04-01


Citation Information: Open Mathematics, Volume 12, Issue 4, Pages 636–647, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0362-1.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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