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Sparse bounds for pseudo-multipliers associated to Grushin operators, II

Sayan Bagchi, Riju Basak, Rahul Garg, Abhishek Ghosh

Abstract

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative weighted estimates for these pseudo-multipliers.

Sparse bounds for pseudo-multipliers associated to Grushin operators, II

Abstract

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative weighted estimates for these pseudo-multipliers.
Paper Structure (23 sections, 27 theorems, 166 equations)

This paper contains 23 sections, 27 theorems, 166 equations.

Table of Contents

  1. Introduction
  2. Pseudo-differential operators on the Euclidean space
  3. Grushin pseudo-multipliers
  4. Main results for classes with
  5. About classes
  6. Joint functional calculus and results for classes
  7. Organisation of the paper
  8. Preliminaries and basic results
  9. Hardy spaces and interpolation
  10. Hardy--Littlewood--Sobolev inequality
  11. Weighted Calderón-Vaillancourt results
  12. Kernel estimates
  13. For pseudo-multipliers associated with
  14. For pseudo-multipliers associated with joint functional calculus
  15. Unweighted boundedness for with
  16. ...and 8 more sections

Key Result

Theorem 1.1

Fix $0< a<1$ and $0\leq \delta<1-a$.

Theorems & Definitions (49)

  • Theorem 1.1: Fefferman Fefferman-Israel-Journal
  • Theorem 1.2: Chanillo--Torchinsky Chanillo-Torchinsky-weighted-pseudodifferential
  • Theorem 1.3: Michalowski--Rule--Staubach Michalowski-Rule-Staubach-Canad2012
  • Definition 1.4
  • Definition 1.5
  • Remark 1.8
  • Theorem 1.9
  • Theorem 1.10
  • Theorem 1.11
  • Definition 1.12
  • ...and 39 more