Abstract and Applied Analysis

Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator

Emin V. Guliyev and Yagub Y. Mammadov

Full-text: Open access

Abstract

We consider the generalized shift operator, associated with the Dunkl operator Λ α ( f ) ( x ) = ( d / d x ) f ( x ) + ( ( 2 α + 1 ) / x ) ( ( f ( x ) - f ( - x ) ) / 2 ) , α > - 1 / 2 . We study some embeddings into the Morrey space ( D -Morrey space) L p , λ , α , 0 λ < 2 α + 2 and modified Morrey space (modified D -Morrey space) L ̃ p , λ , α associated with the Dunkl operator on . As applications we get boundedness of the fractional maximal operator M β , 0 β < 2 α + 2 , associated with the Dunkl operator (fractional D -maximal operator) from the spaces L p , λ , α to L ( ) for p = ( 2 α + 2 - λ ) / β and from the spaces L ̃ p , λ , α ( ) to L ( ) for ( 2 α + 2 - λ ) / β p ( 2 α + 2 ) / β .

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 291345, 10 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620709

Digital Object Identifier
doi:10.1155/2010/291345

Mathematical Reviews number (MathSciNet)
MR2607126

Zentralblatt MATH identifier
1198.46027

Citation

Guliyev, Emin V.; Mammadov, Yagub Y. Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator. Abstr. Appl. Anal. 2010 (2010), Article ID 291345, 10 pages. doi:10.1155/2010/291345. https://projecteuclid.org/euclid.aaa/1288620709


Export citation