INCLUSION THEOREMS IN THE FUNCTION SPACES WITH WIGNER TRANSFORM

Yıl 2022, Cilt: 5 Sayı: 2, 95 - 104, 31.07.2022

Öznur Kulak , Arzu Ömerbeyoğlu

https://doi.org/10.33773/jum.1134775

Öz

In this paper, we consider inclusion relations of $CW_{\omega _{1},\omega
_{2},\omega _{3},\omega _{4}}^{p,q,r,s,\tau }\left(
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right) $ spaces of functions whose Wigner transforms are in weighted
Lebesgue spaces. We then discuss compact embeddings theorems between these
function spaces.

Anahtar Kelimeler

Compact embedding, inclusion, Wigner transform

Destekleyen Kurum

Giresun University

Proje Numarası

FEN-BAPC-150219-01

Kaynakça

• P. Boggiatto, G. De Donno, A. Oliaro, A class of quadratic time- frequency representations based on the short- time Fourier transform, Oper Theory, 172, 235-249 (2007).
• P. Boggiatto, G. De Donno, A. Oliaro, Time- frequency representations of Wigner type and pseudo- differential operators, Trans Amer Math Soc, 362, 4955-4981 (2010).
• M. Duman, O. Kulak. On function spaces with fractional wavelet transform, Montes Taurus J. Pure Appl. Math. 3 (3), 122–134 (2021).
• H.G. Feichtinger, A.T. Gürkanlı, On a family of weighted convolution algebras, Internat. J. Math. Sci. 13(3), 517-526 (1990).
• R. H. Fischer, A.T. Gürkanlı, T.S. Liu, On a family of weighted spaces, Math. Slovaca, 46(1), 71-82 (1996).
• K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Boston, 359s (2001).[7] A.T. Gurkanlı, Compact embeddings of the spaces Apw,Rd, Taiwanese Journal of Mathematics, 12(7), 1757-1767 (2008).
• O. Kulak, A.T. Gürkanlı, On function spaces with wavelet transform in LpωRd × R+, Hacettepe Journal of Mathematics and Statistics, 40(2), 163-177 (2011).
• O. Kulak, A. Ömerbeyoğlu, On function spaces characterized by the Wigner transform, Journal of Universal Mathematics, 4(2), 188-200 (2021).
• O. Kulak, Compact embedding theorems for the space of functions with wavelet transform in amalgam spaces, European Journal of Science and Technology, 28, 568 572 (2021).
• O. Kulak, Compact embedding and inclusion theorems for weighted function spaces with wavelet transform, Lectures of Pure Mathematics on Algebra Analysis and Geometry, Artikel Academy, 41-52 (2021).
• H. Reither, Classical Harmonic Analysis and Locally Compact Group, Oxford Universty Pres, Oxford, 200s (1968).
• A. Sandıkcı, A.T. Gürkanlı, The space ΩpmRd and some properties, Ukrainian Mathematical Journal, 58(1), 155-162 (2006).
• A. Sandıkcı, Continuity of Wigner-type operators on Lorentz spaces and Lorentz mixed normed modulation spaces, Turkish Journal of Mathematics, 38, 728– 745 (201