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Abstract In this paper we study a translation operator associated with the n-dimensional ( k , 1 ) -generalized Fourier transform, where k is a multiplicity function for the Dunkl… Click to show full abstract
Abstract In this paper we study a translation operator associated with the n-dimensional ( k , 1 ) -generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In particular, we prove that the translation is a positivity-preserving operator acting on a suitable space of radial functions on R n . We then use it to define a Hardy-Littlewood type maximal operator, where weak-type ( 1 , 1 ) and strong-type ( p , p ) estimates for the maximal operator are established with a precise behavior in n and k.
Keywords:
generalized fourier;
function;
translation;
translation operator;
fourier transform;
operator
Journal Title: Journal of Functional Analysis
Year Published: 2020
Link to full text (if available)
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Journal Title: Journal of Functional Analysis
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!