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Dergiler / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2018 / Cilt: 67 - Sayı: 2

POTENTIAL OPERATORS ON CARLESON CURVES IN MORREY SPACES

Ahmet EROĞLU, Irada B. DADASHOVA

Sayfa
188–194
DOI
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Abstract

In this paper we study the potential operator I in the Morrey space Lp; and the spaces BMO deÖned on Carleson curves . We prove that for 0 < < 1, I is bounded from the Morrey space Lp;() to Lq;() on simple Carleson curves if (and only if in the inÖnite simple Carleson curve ) 1=p 1=q = =(1 ), 1 < p < (1 )= , and from the spaces L1;() to W Lq;() if (and only if in the inÖnite case) 1 1 q =1-a x.