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On Weighted Iterated Hardy-Type Operators

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Abstract

The weighted L p v − L r ρ boundedness of a weighted iterated Hardy-type operator

$$Tf(x): = {(\int_x^\infty {u(t){{(\int_0^t f )}^q}dt} )^{1/q}}$$

for p = 1 is established.

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Authors and Affiliations

  1. Steklov Mathematical Institute of RAS, 119991, Moscow, Gubkina str. 8, Russia

    V. D. Stepanov

  2. Peoples’ Friendship University of Russia, Miklukho-Maklay 6, 117198, Moscow, Russia

    G. E. Shambilova

Authors
  1. V. D. Stepanov
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  2. G. E. Shambilova
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Correspondence to V. D. Stepanov.

Additional information

This work was supported by the Russian Science Foundation (project no. 16-41-02004) and performed at RUDN University.

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Stepanov, V.D., Shambilova, G.E. On Weighted Iterated Hardy-Type Operators. Anal Math 44, 273–283 (2018). https://doi.org/10.1007/s10476-018-0211-3

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  • DOI: https://doi.org/10.1007/s10476-018-0211-3

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