Open AccessRestriction of Families of Conversion Operators in Lp Spaces
Author(s) -
А. Д. Нахман
Publication year - 2021
Publication title -
vestnik tambovskogo gosudarstvennogo tehničeskogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2542-1409
pISSN - 0136-5835
DOI - 10.17277/vestnik.2021.03.pp.449-460
Subject(s) - mathematics , quasiconvex function , lp space , pure mathematics , limiting , almost everywhere , singular integral operators , convergence (economics) , operator theory , lebesgue integration , mathematical analysis , discrete mathematics , fourier integral operator , banach space , regular polygon , convex analysis , mechanical engineering , geometry , convex optimization , economic growth , economics , engineering
We study a one-parameter family of convolutional operators acting in Lebesgue Lp spaces. The case of integral kernels given by the Fourier coefficients is considered. It is established that the condition of the coefficients being quasiconvex ensures the boundedness of the corresponding maximal operators. The limiting behavior of families in the metrics of spaces of continuous functions and Lp, p ≥ 1, classes is studied, and their convergence is obtained almost everywhere. The ways of possible generalizations and distributions are indicated.