Weighted estimates for oscillatory singular integrals
type: Item
instance of: scholarly article
title: Weighted estimates for oscillatory singular integrals
zbMATH Open document ID: 1268.42021
DOI: 10.1155/2013/543748
author: Yanyan Li
published in: Journal of Function Spaces and Applications
publication date: 2013-05-29T00:00:00Z
review text: Summary: We establish uniform bounds for oscillatory singular integrals as well as oscillatory singular integral operators. We allow the singular kernel to be given by a function in the Hardy space \(H^1(\mathbb S^{n-1})\), while such results were known previously only for kernels in \(L \log L(\mathbb S^{n-1})\), a proper subspace of \(H^1(\mathbb S^{n-1})\). One of our results establishes a \(L^p(w) \to L^p(w)\) bound for certain weights. At the same time, it provides a solution to an open problem stated in [\textit{S. Lu}, Int. J. Appl. Math. Sci. 2, No. 1, 47--64 (2005; Zbl 1078.42006)].
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 6167903
zbMATH Keywords: oscillatory singular integral
Wikidata QID: Q59014378
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/543748
OpenAlex ID: W1994158420
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description: scientific article; zbMATH DE number 6167903