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Mathematics > Classical Analysis and ODEs
Title: Weighted norm inequalities for integral transforms with splitting kernels
(Submitted on 27 Dec 2023 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable.
The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the $\mathscr{H}_\alpha$ (or Struve) transform in the case $\alpha>\frac{1}{2}$, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases $p=1$ or $q=\infty$.
Submission history
From: Alberto Debernardi Pinos [view email][v1] Wed, 27 Dec 2023 11:34:34 GMT (19kb)
[v2] Sun, 3 Mar 2024 15:38:15 GMT (19kb)
[v3] Fri, 26 Apr 2024 06:55:39 GMT (62kb)
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