Startseite Mathematik Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
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Weighted estimates for product singular integral operators in Journé’s class on RD-spaces

  • Taotao Zheng ORCID logo EMAIL logo , Yanmei Xiao und Xiangxing Tao
Veröffentlicht/Copyright: 18. April 2024
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 37 Heft 2

Abstract

An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–PĂŽlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.

Keywords: Singular integral operator; product weighted Triebel–Lizorkin space; product weighted Besov space; Hardy space; Lipschitz space; Carleson measure space
MSC 2020: 42B20; 42B25; 46E35

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12326307

Award Identifier / Grant number: 12326308

Award Identifier / Grant number: 12271483

Funding source: Natural Science Foundation of Zhejiang Province

Award Identifier / Grant number: LQ17A010002

Funding statement: This research was funded by National Natural Science Foundation of China (grant numbers 12326307, 12326308, 12271483) and Natural Science Foundation of Zhejiang Province (grant number LQ17A010002).

  1. Communicated by: Christopher D. Sogge

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Received: 2023-07-29
Revised: 2024-03-16
Published Online: 2024-04-18
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
  3. Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
  4. Estimates of Picard modular cusp forms
  5. Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
  6. Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
  7. Free groups generated by two unipotent maps
  8. Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
  9. Colored multizeta values in positive characteristic
  10. Simultaneous nonvanishing of central L-values with large level
  11. Laplace convolutions of weighted averages of arithmetical functions
  12. Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
  13. On the geometric trace of a generalized Selberg trace formula
  14. Elementary properties of free lattices
  15. Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
  16. Small generators of abelian number fields
  17. Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
  18. Weighted bilinear multiplier theorems in Dunkl setting via singular integrals
https://doi.org/10.1515/forum-2023-0273
Schlagwörter fĂŒr diesen Artikel
Singular integral operator; product weighted Triebel–Lizorkin space; product weighted Besov space; Hardy space; Lipschitz space; Carleson measure space

Artikel in diesem Heft

  1. Frontmatter
  2. Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
  3. Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
  4. Estimates of Picard modular cusp forms
  5. Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
  6. Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
  7. Free groups generated by two unipotent maps
  8. Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
  9. Colored multizeta values in positive characteristic
  10. Simultaneous nonvanishing of central L-values with large level
  11. Laplace convolutions of weighted averages of arithmetical functions
  12. Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
  13. On the geometric trace of a generalized Selberg trace formula
  14. Elementary properties of free lattices
  15. Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
  16. Small generators of abelian number fields
  17. Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
  18. Weighted bilinear multiplier theorems in Dunkl setting via singular integrals
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