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Strong summability for the Marcinkiewicz means in the integral metric and related questions

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

E. S. Belinsky
E. S. Belinsky
Affiliation:
Department of Mathematics, University of Zimbabwe, Harare, Zimbabwe e-mail: belinsky@maths.uz.ac.zw
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Abstract

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The inequality of strong summability for the Marcinkiewicz means of multiply Fourier series is proved. The inequalities of strong summability with gaps for the different classes of integrable functions are established. The Bernstein inequality for the fractional derivative of analytic polynomials is proved.

Keywords

Marcinkiewicz meansstrong summabilityBernstein inequality

MSC classification

Secondary: 42A24: Summability and absolute summability of Fourier and trigonometric series
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 303 - 312
Copyright
Copyright © Australian Mathematical Society 1998

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