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Existence of convolution maximizers in $L_p(R^n)$ for kernels from Lorentz spacesстатья
- Автор: Sadov Sergey
- Журнал: ArXiv e-prints
- Год издания: 2022
- Первая страница: 1
- Последняя страница: 11
- Номер статьи: arXiv:2208.08783 [math.FA]
- DOI: 10.48550/ARXIV.2208.08783
- Аннотация: The paper extends an earlier result of G.V.~Kalachev and the author (Sb. Math. 2019 or arXiv:1712.08836) on the existence of a maximizer of convolution operator acting between two Lebesgue spaces on Rn with kernel from some Lq, 1<q<∞. In view of Lieb's result of 1983 about the existence of an extremizer for the Hardy-Littlewood-Sobolev inequality it is natural to ask whether a convolution maximizer exists for any kernel from weak Lq. The answer in the negative was given by Lieb in the above citation. In this paper we prove the existence of maximizers for kernels from a slightly more narrow class than weak Lq, which contains all Lorentz spaces L_{q,s} with q ≤ s < ∞.
- Добавил в систему: Садов Сергей Юрьевич