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Yayın A multiplier related to symmetric stable processes(Hacettepe University, 2017) Karlı, DenizIn two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some boundedness conditions with weaker hypotheses. In this paper, we study a multiplier theorem using these more general results. We consider a product process consisting of a d-dimensional symmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms and the Lp(Rd)-norm of a new operator.Yayın Extension of mikhlin multiplier theorem to fractional derivatives and stable processes(Walter De Gruyter GMBH, 2018-04-25) Karlı, DenizIn 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.
