Improvement of smoothness of functions by bilinear operators, continuous by measure

A.M. Pas'ko (Oles Honchar Dnipropetrovsk National University)

Abstract


The sequences of the translation invariant by the both arguments, continuous bilinear operators $$$T_n\colon L_1 \times L_1 \rightarrow L_0$$$ has been considered. The improvement of the smoothness of the functions belonging to the Lipschitz-Holder classes has been established.

Keywords


bilinear operators; translation invariant; smooth functions

References


Pas'ko A.M. "Bilinear operators, continuous by measure", Dnipr. Univ. Math. Bull., 2002; 7: pp. 60-72. (in Ukrainian)

Pichugov S.A. "Stein theorem for operators bounded by measure", Dnipr. Univ. Math. Bull., 2002; 7: pp. 82-83. (in Ukrainian)

Timan A.F. Approximation theory for real-variable functions, Fizmatgiz, Moscow, 1960; 624 p. (in Russian)

Edwards R.E. Functional analysis, Mir, Moscow, 1969; 1072 p. (in Russian)


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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557