Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator
Keyword(s):
We consider the generalized shift operator, associated with the Dunkl operatorΛα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2),α>-1/2. We study some embeddings into the Morrey space (D-Morrey space)Lp,λ,α,0≤λ<2α+2and modified Morrey space (modifiedD-Morrey space)L̃p,λ,αassociated with the Dunkl operator onℝ. As applications we get boundedness of the fractional maximal operatorMβ,0≤β<2α+2, associated with the Dunkl operator (fractionalD-maximal operator) from the spacesLp,λ,αtoL∞(ℝ)forp=(2α+2-λ)/βand from the spacesL̃p,λ,α(ℝ)toL∞(ℝ)for(2α+2-λ)/β≤p≤(2α+2)/β.
2013 ◽
Vol 21
(2)
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pp. 111-130
2004 ◽
Vol 21
(1)
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pp. 53-64
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Keyword(s):
2008 ◽
Vol 109
(2)
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pp. 591-598
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2021 ◽
Vol 101
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pp. 17-24