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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences

THE CONVOLUTION IN ANISOTROPIC TRIEBEL–LIZORKIN SPACES

Published June 2021

97

102

N.T. Tleukhanova +
L.N. Gumilyov Eurasian National University, Nur-Sultan
K.K. Sadykova +
L.N. Gumilyov Eurasian National University, Nur-Sultan
L.N. Gumilyov Eurasian National University, Nur-Sultan
L.N. Gumilyov Eurasian National University, Nur-Sultan
Abstract

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.

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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.