img
img
Necessary and sufficient conditions for the boundedness of B-Riesz potential in the B-Morrey spaces   
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi
Javanshir J. Hasanov
Devamını Göster
Özet
We consider the generalized shift operator, associated with the Laplace-Bessel differential operator Delta(B) = Sigma(n)(i=1) partial derivative(2)/partial derivative x(i)(2) + Sigma(k)(i=1) gamma(i)/x(i) partial derivative/partial derivative x(i). The maximal operator M-gamma (B-maximal operator) and the Riesz potential I-gamma(alpha) (B-Riesz potential), associated with the generalized shift operator are investigated. At first, we prove that the B-maximal operator M-gamma is bounded from the B-Morrey space L-p,L-lambda,L-gamma to L-p,L-lambda,L-gamma for all 1 < p < infinity and 0 <= lambda < n + vertical bar gamma vertical bar. We prove that the B-Riesz potential I-gamma(alpha), 0 < alpha < vertical bar gamma vertical bar is bounded from the B-Morrey space L-p,L-lambda,L-gamma to L-q,L-lambda,L-gamma if and only if alpha/(n+vertical bar gamma vertical bar - lambda) = 1/p - 1/q, 1 < p < (n + vertical bar gamma vertical bar - lambda)/alpha. Also we prove that the B-Riesz potential I-gamma(alpha) is bounded from the B-Morrey space L-1,L-lambda,L-gamma to the weak B-Morrey space WLq,lambda,gamma if and only if alpha/(n + vertical bar gamma vertical bar - lambda) = 1 - 1/q.
Anahtar Kelimeler
B-maximal operator | B-Morrey space | B-Riesz potential | Hardy-Littlewood-Sobolev-Morrey type estimate
Makale Türü Özgün Makale
Makale Alt Türü SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale
Dergi Adı JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Dergi ISSN 0022-247X Wos Dergi Scopus Dergi
Dergi Grubu Q1
Makale Dili İngilizce
Basım Tarihi 11-2008
Cilt No 347
Sayı 1
Sayfalar 113 / 122
Doi Numarası 10.1016/j.jmaa.2008.03.077