Spaces of DLp type and a convolution product associated with the spherical mean operator

Abstract

We define and study the spacesUsing the harmonic analysis associated with the spherical mean operator, we give a new characterization of the dual space ᏹ p (R × R n ) and describe its bounded subsets. Next, we define a convolution product inand prove some new results.

Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications

“…In this section, we collect some harmonic analysis results related to the operator Δ . For details, we refer the reader to [1,[4][5][6][7][8].…”

Homogeneous Besov Spaces associated with the spherical mean operator

“…The spherical mean operator R and its dual t R play an important role and have many applications, for example, in image processing of so-called synthetic aperture radar (SAR) data [14,15], or in the linearized inverse scattering problem in acoustics [9]. Many aspects of such operator have been studied [1,3,6,18,21]. In particular, in [18] the first author with the others associated to the spherical mean operator the Fourier transform defined by ∀(µ, λ) ∈ Γ, F (f)(µ, λ) = r n dr ⊗ dx.…”