General Hormander and Mikhlin conditions for multipliers of Besov spaces

TL;DR

This paper introduces new geometric conditions for Banach spaces and establishes Fourier multiplier theorems in weighted Besov spaces, linking geometry with Hormander-Mikhlin conditions and applying results to elliptic differential equations.

Contribution

It presents novel geometric conditions for Banach spaces and derives Fourier multiplier theorems in weighted Besov spaces, connecting geometry with Hormander-Mikhlin conditions.

Findings

New geometric conditions for Banach spaces introduced

Fourier multiplier theorems in weighted Besov spaces established

Applications to regularity of degenerate elliptic differential operators

Abstract

Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated.