Bochner-Riesz Means at the Critical Index: Weighted and Sparse Bounds
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Date
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Volume
16
Issue
Journal
Series Titel
Oberwolfach Preprints (OWP)
Book Title
Publisher
Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
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Abstract
We consider Bochner-Riesz means on weighted Lp spaces, at the critical index λ(p)=d(1/p−1/2)−1/2. For every A₁-weight we obtain an extension of Vargas' weak type (1,1) inequality in some range of p>1. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension d=2; partial results as well as conditional results are proved in higher dimensions. For the means of index λ∗=(d−1)/(2d+2) we prove fully optimal sparse bounds.
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Keywords
Bochner-Riesz Means, Sparse Domination, Endpoint Estimates, Weighted Norm Estimates, Convergence in Weighted Spaces
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.