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THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS    
Yazarlar (4)
A. D. Gadjiev
Prof. Dr. Vagıf GULIYEV Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi
A. Serbetci
E. V. Guliyev
Devamını Göster
Özet
We establish two inequalities of Stein-Weiss type for the Riesz potential operator I-alpha,I-gamma (B-Riesz potential operator) generated by the Laplace-Bessel differential operator Delta B in the weighted Lebesgue spaces L-p,L-vertical bar x vertical bar beta,L-gamma. We obtain necessary and sufficient conditions on the parameters for the boundedness of Ia,. from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to L-q,L-vertical bar x vertical bar-lambda,L-gamma, and from the spaces L-1,L-vertical bar x vertical bar beta,L-gamma to the weak spaces WLq,vertical bar x vertical bar-lambda,gamma. In the limiting case p = Q/alpha we prove that the modified B-Riesz potential operator (I) over tilde (alpha,gamma) is bounded from the spaces L-p,L-vertical bar x vertical bar beta,L-gamma to the weighted B-BMO spaces BMO vertical bar x vertical bar-lambda,gamma.
As applications, we get the boundedness of I-alpha,I-gamma from the weighted B-Besov spaces B-p theta,vertical bar x vertical bar beta,gamma(s) to the spaces B-q theta,vertical bar x vertical bar-lambda,gamma(s). Furthermore, we prove two Sobolev embedding theorems on weighted Lebesgue L-p,L-vertical bar x vertical bar beta,L-gamma and weighted B-Besov spaces B-p theta,vertical bar x vertical bar beta,gamma(s) by using the fundamental solution of the B-elliptic equation Delta(alpha/2)(B)
Anahtar Kelimeler
B-Riesz potential | Laplace-Bessel differential operator | Stein-weiss type inequalities | Weighted B-Besov space | Weighted lebesgue space
Makale Türü Özgün Makale
Makale Alt Türü SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale
Dergi Adı JOURNAL OF MATHEMATICAL INEQUALITIES
Dergi ISSN 1846-579X Wos Dergi Scopus Dergi
Dergi Grubu Q1
Makale Dili İngilizce
Basım Tarihi 03-2011
Cilt No 5
Sayı 1
Sayfalar 87 / 106
Doi Numarası 10.7153/jmi-05-09