In this paper, we investigate the boundedness of the norm of the convolution operator in anisotropic Triebel-Lizorkin spaces. The Triebel-Lizorkin spaces are based on the Lorentz spaces pq L . In the anisotropic case, we take the anisotropic Lorentz space pq L as the base. The main goal of the paper is to solve the following problem: let f and g be functions from some classes of the Triebel-Lizorkin space scale. It is necessary to determine which conditions on the parameters of the spaces from f and g are taken and study which space belongs to their convolution gf . An analogue of the O'Neil theorem was obtained for the Triebel-Lizorkin space scale αq pτF , where α , τ, p , q are vector parameters. Relations of the form γξ hν βη rμ F F ↪ αq pτF are obtained, with the corresponding ratios of vector
parameters γ βα ,
hrp 11 1 1 ,
νμτ 111 ,
ηξq 111 . The research method is the functional spaces theory
and inequalities of functional and harmonic analysis.
THE CONVOLUTION IN ANISOTROPIC TRIEBEL–LIZORKIN SPACES
Published June 2021
97
102
Abstract
Language
English
How to Cite
[1]
Tleukhanova , N. and Sadykova , .K. 2021. THE CONVOLUTION IN ANISOTROPIC TRIEBEL–LIZORKIN SPACES . Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 69, 1 (Jun. 2021), 163–168.