On fractional maximal function and fractional integrals associated with the Dunkl operator on the real line

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:353

Article

Guiyev, Vagif S.^1,2  Mammadov, Yagub Y.^3,4 

[1] Azerbaijan Acad Sci, Inst Math & Mech, Baku, Azerbaijan

[2] Baku State Univ, Dept Math Anal, Baku, Azerbaijan

[3] Nakhchivan State Univ, Nakhchivan, Azerbaijan

[4] Nakhchivan Teacher Training Inst, Nakhchivan, Azerbaijan

关键词: Dunkl operator;    Dunkl-type fractional maximal operator;    Dunkl-type fractional integral operator;    Dunkl-type BMO space;    Dunkl-type Besov spaces;   

DOI  :  10.1016/j.jmaa.2008.11.083

来源: Elsevier

【 摘 要 】

In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the Dunkl-type fractional maximal operator M(beta), and the Dunkl-type fractional integral operator I(beta) from the spaces L(p,alpha)(R) to the spaces L(q,alpha)(R), 1 (beta) is bounded from the space L(p,alpha)(R) to the Dunkl-type BMO space BMO(alpha)(R). By this results we get boundedness of the operators M(beta) and I(beta) from the Dunkl-type Besov spaces B(p theta,alpha)(s)(R) to the spaces B(p theta,alpha)(s)(R), 1 <=infinity and 0<1. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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