Some results on generalized Dunkl–Lipschitz spaces

Abstract

In this paper we study certain relations between the Dunkl-Sobolev classes of fractional order  , ( ) and the generalized Dunkl-Lipschitz classes ∧ , , ( ). Next, we show a Dunkl-Hardy-Littlewood theorem for -temperatures and its dual. Also, we give some theorems on Dunkl convolutions of Dunkl-Lipschitz functions. Finally, we establish some results concerning the Dunkl transforms of functions and distributions belonging to generalized Dunkl-Lipschitz spaces. K E Y W O R D SDunkl operator, Dunkl transform, generalized Dunkl-Lipschitz space, maximal functions M S C ( 2 0 1 0 ) 26A16, 42A38, 42B25, 46E30 www.mn-journal.org