Extension of Mikhlin Multiplier Theorem to Fractional Derivatives and Stable Processes
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.09975
- arXiv:
- arXiv:1806.09975
- Bibcode:
- 2018arXiv180609975K
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Functional Analysis;
- Primary 60J45;
- Secondary 42A61;
- 60G52;
- 26A33
- E-Print:
- 23 pages