Methods and Applications of Analysis

Volume 26 (2019)

Number 4

Realizations of the homogeneous Besov-type spaces

Pages: 349 – 370

DOI: https://dx.doi.org/10.4310/MAA.2019.v26.n4.a3

Authors

Fares Bensaid (Laboratory of Functional Analysis and Geometry of Spaces, Mohamed Boudiaf University of M’Sila, Algeria)

Madani Moussai (Laboratory of Functional Analysis and Geometry of Spaces, Mohamed Boudiaf University of M’Sila, Algeria)

Abstract

Using the notion of realizations, we study the dilation commuting realizations of the homogeneous Besov-type spaces $\dot{B} \begin{smallmatrix} s, & \tau \\ p, & q \end{smallmatrix} (\mathbb{R}^n)$, which are defined modulo polynomials of degree less than $\mu$; the integer $\mu$ will be determined from the parameters $n$, $s$, $p$, $q$ and $\tau$.

Keywords

Littlewood–Paley decomposition, distributions modulo polynomials, homogeneous Besov-type spaces

2010 Mathematics Subject Classification

46E35

Received 18 July 2017

Accepted 16 August 2019

Published 13 May 2020