The convolution in anisotropic Besov spaces

Вестник КазНУ. Серия математика, механика, информатика

N.T. Tleukhanova¹  K.K. Sadykova¹ 

[1] L.N. Gumilyov Eurasian National University;

关键词: young-o’neil inequality;    anisotropic besov spañes;    convolution operator;   

DOI  :  https://doi.org/10.26577/JMMCS.2020.v106.i2.02

来源: DOAJ

【 摘 要 】

We study the boundedness of the convolution operator in Nikol’skii-Besov anisotropic spacesBαqpτ.These spaces are constructed on the basis of anisotropic Lorentz spacesLpτ, wherepиτare vectorparameters. The properties of anisotropic Nikol’skii-Besov spaces are investigated. The main goalof the paper is to solve the following problem: letfandgbe functions from some classes of theNikol’skii-Besov space scale. It is necessary to determinewhich space belongs to their convolutionf∗g. We prooved the inequality of different Nikol’skii metrics for trigonometric polynomials withspectrum in binary blocks in anisotropic Lorentz spacesLpτ. Conditions are obtained in terms ofthe corresponding vector parametersα,p,q,τ,r,μ,β,η,h,ν,γ,ξ, which are necessary andsufficient conditions for embeddingsBβηrμ∗Bγξhν֒→Bαqpτ.This statement is an analogue of O’Neil inequality for Lorentz spaces. In particular, the clas-sical O’Neil inequality follows from the proved results. The obtained criterion is generalized bythe results of Burenkov and Batyrov, who considered this problem in Besov spaces with scalarparameters.

【 授权许可】

Unknown