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On the geometric mean operator with variable limits of integration

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Abstract

A new criterion for the weighted L p −L q boundedness of the Hardy operator with two variable limits of integration is obtained for 0 < q < q + 1 ≤ p < ∞. This criterion is applied to the characterization of the weighted L p −L q boundedness of the corresponding geometric mean operator for 0 < q < p < ∞.

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Author notes

  1. E. P. Ushakova

    Present address: Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden

Authors and Affiliations

  1. Department of Mathematical Analysis and Function Theory, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    V. D. Stepanov

  2. Computing Centre, Far East Branch of the Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680063, Russia

    E. P. Ushakova

Authors
  1. V. D. Stepanov
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  2. E. P. Ushakova
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Correspondence to V. D. Stepanov.

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Original Russian Text © V.D. Stepanov, E.P. Ushakova, 2008, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 260, pp. 264–288.

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Stepanov, V.D., Ushakova, E.P. On the geometric mean operator with variable limits of integration. Proc. Steklov Inst. Math. 260, 254–278 (2008). https://doi.org/10.1134/S0081543808010185

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  • DOI: https://doi.org/10.1134/S0081543808010185

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