Copy For Citation
Guliyev V. S., Hasanov J. J., ZEREN Y.
JOURNAL OF MATHEMATICAL INEQUALITIES, vol.5, no.4, pp.491-506, 2011 (SCI-Expanded)
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Publication Type:
Article / Article
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Volume:
5
Issue:
4
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Publication Date:
2011
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Doi Number:
10.7153/jmi-05-43
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Journal Name:
JOURNAL OF MATHEMATICAL INEQUALITIES
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Journal Indexes:
Science Citation Index Expanded (SCI-EXPANDED), Scopus
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Page Numbers:
pp.491-506
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Keywords:
Riesz potential, fractional maximal function, modified Morrey space, Hardy-Littlewood-Sobolev inequality, Schodinger type operator, WEIGHTED NORM INEQUALITIES, SCHRODINGER-OPERATORS
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Yıldız Technical University Affiliated:
Yes
Abstract
We prove that the fractional maximal operator M-alpha and the Riesz potential operator I-alpha, 0 < alpha < n are bounded from the modified Morrey space (L) over tilde (1,lambda) (R-n) to the weak modified Morrey space W (L) over tilde (q,lambda) (R-n) if and only if, alpha/n <= 1 - 1/q <= alpha/(n - lambda) and from (L) over tilde (p,lambda) (R-n) to (L) over tilde (q,lambda) (R-n) if and only if, alpha/n <= 1/p - 1/q <= alpha/(n - lambda).