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Weak type (1,1) in a refinement of the Marcinkiewicz theorem

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Abstract

Let m be a bounded function on ℝ+ whose p-variations on the intervals [2k, 2k+1], k ∈ ℤ, are uniformly bounded for some p < 2. Then the operator T, \( \widehat{Tf} = m\hat f \), is of weak type (1, 1) on the space H 1(ℝ).

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Authors and Affiliations

  1. St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

    S. V. Kislyakov

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  1. S. V. Kislyakov
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Correspondence to S. V. Kislyakov.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 43, No. 3, pp. 89–92, 2009

Original Russian Text Copyright © by S. V. Kislyakov

To the memory of Professor Solomon Grigorievich Mikhlin

Supported by RFBR grant no. 08-01-00358.

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Kislyakov, S.V. Weak type (1,1) in a refinement of the Marcinkiewicz theorem. Funct Anal Its Appl 43, 236–238 (2009). https://doi.org/10.1007/s10688-009-0030-1

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  • DOI: https://doi.org/10.1007/s10688-009-0030-1

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