On new sharp theorems on Toeplits operators in Lizorkin–Triebel spaces
https://doi.org/10.25587/2411-9326-2025-2-56-64
Abstract
In this short note we provided new sharp results concerning the action of so called integral Toeplits operators in holomorphic Lizorkin-Triebel function spaces in the unit polydisk. Holomorphic function spaces of Lizorkin-Triebel type in the unit polydisk extend well known Bergman and Hardy spaces simultuanously. Because of this it is interesting to study these new spaces in higher dimension. Our results may have various interesting applications in complex function theory. Of one and several complex variables. Our proofs in particular are based on several standard estimates of complex function theory of several complex variables. We also mention that Toeplits operators were mainly studied previously only in one dimension namely in the unit disk case. Our results may have also interesting applications in operator theory.
About the Authors
R. F. Shamoyan
Saratov State University
Russian Federation
Russian Federation
Romy F. Shamoyan
83 Astrakhanskaya Street, Saratov 410012
E. B. Tomashevskaya
Bryansk State Technical University
Russian Federation
Russian Federation
Elena B. Tomashevskaya
43 Bezhitskaya Street, Bryansk 241050
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Review
For citations:
Shamoyan R.F., Tomashevskaya E.B. On new sharp theorems on Toeplits operators in Lizorkin–Triebel spaces. Mathematical notes of NEFU. 2025;32(2):56-64. https://doi.org/10.25587/2411-9326-2025-2-56-64
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