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Weighted Dunkl transform inequalities and application on radial Besov spaces

Weighted Dunkl transform inequalities and application on radial Besov spaces In Dunkl theory on $$\mathbb R ^d$$ which generalizes classical Fourier analysis, we prove first weighted inequalities for certain Hardy-type averaging operators. In particular, we deduce for specific choices of the weights the $$d$$ -dimensional Hardy inequalities whose constants are sharp and independent of $$d$$ . Second, we use the weight characterization of the Hardy operator to prove weighted Dunkl transform inequalities. As consequence, we obtain Pitt’s inequality which gives an integrability theorem for this transform on radial Besov spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

Weighted Dunkl transform inequalities and application on radial Besov spaces

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-013-0180-1
Publisher site
See Article on Publisher Site

Abstract

In Dunkl theory on $$\mathbb R ^d$$ which generalizes classical Fourier analysis, we prove first weighted inequalities for certain Hardy-type averaging operators. In particular, we deduce for specific choices of the weights the $$d$$ -dimensional Hardy inequalities whose constants are sharp and independent of $$d$$ . Second, we use the weight characterization of the Hardy operator to prove weighted Dunkl transform inequalities. As consequence, we obtain Pitt’s inequality which gives an integrability theorem for this transform on radial Besov spaces.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals

Published: Mar 27, 2013

References

  • Besov-type spaces on $$\mathbb{R}^d $$ and integrability for the Dunkl transform. Symmetry, Integrability and Geometry: Methods and Applications
    Abdelkefi, C; Anker, J; Sassi, F; Sifi, M
  • Dunkl operators on $$\mathbb{R}^d$$ and uncentered maximal function
    Abdelkefi, C
  • Weighted Fourier inequalities: new proofs and generalizations
    Benedetto, JJ; Heinig, HP
  • Interpolation of Operators
    Bennett, C; Sharpley, R
  • The Dunkl transform
    Jeu, MFE
  • Higher dimensional Hardy inequality. (Oberwolfach, 1995)
    Drabek, P; Heinig, HP; Kufner, A
  • Differential-difference operators associated to reflection groups
    Dunkl, CF
  • Integral kernels with reflection group invariance
    Dunkl, CF
  • Orthogonal polynomials of several variables
    Dunkl, CF; Xu, Y
  • Best constants for two nonconvolution inequalities
    Christ, M; Grafakos, L
  • Note on a theorem of Hilbert
    Hardy, GH
  • Inequalities
    Hardy, GH; Littlewood, JE; Pólya, G
  • Weighted norm inequalities for classes of operators
    Heinig, HP
  • Inequalities for the Fourier transform
    Jodeit, M; Torchinsky, A
  • Sobolev Spaces
    Maz’ja, VG
  • Markov processes with Dunkl operators
    Rösler, M; Voit, M
  • A positive radial product formula for the Dunkl kernel
    Rösler, M
  • Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
    Stein, EM
  • Convolution operator and maximal function for Dunkl transform
    Thangavelyu, S; Xu, Y
  • Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators
    Trimèche, K