Taiwanese Journal of Mathematics

COMPACT EMBEDDINGS OF THE SPACES Ap w,ω

A. Turan G¨urkanll

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Abstract

For $1\leq p\leq \infty , A_{w,\omega }^{p}\left( R^{d}\right) $ denotes the space (Banach space) of all functions in $L_{w}^{1}\left( R^{d}\right) $ a weighted $L^{1}-$space (Beurling algebra) with Fourier transforms $\overset{\wedge }{f}$ in\ $L_{\omega }^{p}\left( R^{d}\right) $ which is equipped with the sum norm \begin{equation*} \left\Vert f\right\Vert _{w,\omega }^{p}=\left\Vert f\right\Vert _{1,w}+\left\Vert \overset{\wedge }{f}\right\Vert _{p,\omega }, \end{equation*}% where $w$ and $\omega $ are Beurling weights on $R^{d}$.This space was defined in $\left[ 5\right] $ and generalized in $\left[ 6\right] .$ The present paper is a sequal to these works.In this paper we are going to discuss compact embeddings between the spaces $A_{w,\omega }^{p}\left( R^{d}\right) .$

Article information

Source
Taiwanese J. Math., Volume 12, Number 7 (2008), 1757-1767.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405086

Digital Object Identifier
doi:10.11650/twjm/1500405086

Mathematical Reviews number (MathSciNet)
MR2449663

Subjects
Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

Keywords
weighted $L^{p}-$spaces Beurling algebra compact embedding

Citation

G¨urkanll, A. Turan. COMPACT EMBEDDINGS OF THE SPACES Ap w,ω. Taiwanese J. Math. 12 (2008), no. 7, 1757--1767. doi:10.11650/twjm/1500405086. https://projecteuclid.org/euclid.twjm/1500405086


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References

  • P. Boggiatto and J. Toft, Embeddings and compactness for generalized Sobolev -Shubin spaces and modulation spaces, Applicable Analysis, 84(3) (2005), 269-282.
  • J. Dieudonne, Treatise on analysis, Volume 2, Academic Press, New York- San Francisco-London, 1976.
  • M. Dogan and A. T. Gürkanlriptsize l, Multipliers of the space $S_{\omega } (G),$ Mathematica Balkanica, New Series, 15(3-4) (2001), 200-212.
  • M. Doğan and A. T. Gürkanlriptsize l, On functions with Fourier transforms in $S_{w}$, Bull. Cal. Math. Soc. 92(2) ( 2000), 111-120.
  • H. G. Feichtinger and A. T. Gürkanlriptsize l, On a family of Weighted Convolution Algebras, Internat. J. Math. and Math. Sci., 13(3) (1990), 517-526.
  • R. H. Fischer, A. T. Gürkanlriptsize l and T. S. Liu, On family of Weighted Spaces, Math. Slovaca., 46(1) (1996), 71-82.
  • G. I.Gaudry, Multipliers of Weighted Lebesgue and Measure Spaces, Proc. Lon. Math. Soc., 19(3) (1969), 327-340.
  • A. T. Gürkanlriptsize l, Some results in the weighted $A_{p}(\mathbb{R}^{n})$ spaces, Demonstratio Mathematica, XIX, \bf (4) (1986), 825-830.
  • A. T. Gürkanlriptsize l, Multipliers of some Banach ideals and Wiener-Ditkin sets, Math. Slovaca., 55(2)(2005), 237-248.
  • R. Larsen, T. Liu and J. Wang, On functions with Fourier transform in $L_{p}$, Michigan Math. Journal., 11 (1964), 369-378.
  • H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press, Oxford, 1968.
  • W. Rudin, Fourier Analysis on Groups, Interscience Publishers, New York, 1962.
  • J. C. Martin and L. Y. H. Yap, The algebra of functions with Fourier transform in $L^{p},$ Proc. Amer. Math. Soc., 24 (1970), 217-219.