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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

IMPACT FACTOR 2018: 3.514
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CiteScore 2018: 3.44

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Volume 21, Issue 2


Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes

Deniz Karlı
  • Department of Mathematics, Işık University AMF233, 34980 Şile, Istanbul, TURKEYdeniz.karli@isikun.edu.tr (secondary)
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Published Online: 2018-06-09 | DOI: https://doi.org/10.1515/fca-2018-0027


In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between fractional derivatives and stable processes and prove a version of Mikhlin theorem under a condition given in terms of the infinitesimal generator of symmetric stable process. The classical Mikhlin theorem is shown to be a corollary of this new generalized version in this paper.

MSC 2010: Primary 60J45; Secondary 42A61, 60G52, 26A33

Key Words and Phrases: fractional derivatives; generator form; Mikhlin multiplier theorem; stable process; bounded operator; stochastic process


About the article

Received: 2017-02-03

Published Online: 2018-06-09

Published in Print: 2018-04-25

Citation Information: Fractional Calculus and Applied Analysis, Volume 21, Issue 2, Pages 486–508, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2018-0027.

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