O. L. Vinogradov, “A boundedness criterion for averaging operators in variable exponent spaces of periodic functions”, Investigations on linear operators and function theory. Part 52, Zap. Nauchn. Sem. POMI, 537, POMI, St. Petersburg, 2024, 40

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Zapiski Nauchnykh Seminarov POMI, 2024, Volume 537, Pages 40–63 (Mi znsl7516)

A boundedness criterion for averaging operators in variable exponent spaces of periodic functions

O. L. Vinogradov

Saint Petersburg State University

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Abstract: A criterion for the uniform boundedness of Steklov averaging operators in variable exponent spaces of periodic functions is obtained. This criterion coincides with the known local analog of the Muckenhoupt condition. The boundedness of Steklov averages was previously known under the Dini–Lipschitz condition. The norms of averaging operators are estimated explicitly.

Key words and phrases: variable exponent spaces, Steklov averages.

Funding agency	Grant number
Russian Science Foundation	23-11-00178

Received: 30.09.2024

Document Type: Article

UDC: 517.5

Language: Russian

Citation: O. L. Vinogradov, “A boundedness criterion for averaging operators in variable exponent spaces of periodic functions”, Investigations on linear operators and function theory. Part 52, Zap. Nauchn. Sem. POMI, 537, POMI, St. Petersburg, 2024, 40–63

Citation in format AMSBIB

\Bibitem{Vin24}

\by O.~L.~Vinogradov

\paper A boundedness criterion for averaging operators in variable exponent spaces of periodic functions

\inbook Investigations on linear operators and function theory. Part~52

\serial Zap. Nauchn. Sem. POMI

\yr 2024

\vol 537

\pages 40--63

\publ POMI

\publaddr St.~Petersburg

\mathnet{http://mi.mathnet.ru/znsl7516}

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