THE STEIN-WEISS TYPE INEQUALITIES FOR THE <i>B</i>-RIESZ POTENTIALS

Gadjiev, A. D.; GULIYEV, VAGIF; Serbetci, A.; Guliyev, E. V.

doi:10.7153/jmi-05-09

THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS

Yazarlar (4)

A. D. Gadjiev Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan

Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye

A. Serbetci Ankara Üniversitesi, Türkiye

E. V. Guliyev Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan

Makale Türü	Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
Dergi Adı	Journal of Mathematical Inequalities (Q1)
Dergi ISSN	1846-579X Wos Dergi Scopus Dergi
Makale Dili	İngilizce	Basım Tarihi	03-2011
Cilt / Sayı / Sayfa	5 / 1 / 87–106	DOI	10.7153/jmi-05-09
Makale Linki	http://www.scopus.com/inward/record.url?eid=2-s2.0-79958296179&partnerID=MN8TOARS

Özet

We establish two inequalities of Stein-Weiss type for the Riesz potential operator Iα,γ (B-Riesz potential operator) generated by the Laplace-Bessel differential operator ΔB in the weighted Lebesgue spaces Lp,|x|β,γ. We obtain necessary and sufficient conditions on the parameters for the boundedness of Iα,γ from the spaces Lp,|x|β,γ to Lq,|x|-λ,γ, and from the spaces L1,|x|β,γ to the weak spaces WLq,|x|-λ,γ. In the limiting case p=Q/α we prove that the modified B-Riesz potential operator Iα,γ is bounded from the spaces Lp,|x|β,γ to the weighted B-BMO spaces BMO|x|-λ,γ. As applications, we get the boundedness of Iα,γ from the weighted B-Besov spaces B^spΘ,|x|β,γ to the spaces B^sqΘ,|x|-λ,γ. Furthermore, we prove two Sobolev embedding theorems on weighted Lebesgue Lp,|x|β,γ and weighted B-Besov spaces B^spΘ,|x|β,γ by using the fundamental solution of the B-elliptic equation Δ^α/2B.

Anahtar Kelimeler

B-Riesz potential | Laplace-Bessel differential operator | Stein-weiss type inequalities | Weighted B-Besov space | Weighted lebesgue space

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Atıf Sayıları

THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS

Dergi Adı	Journal of Mathematical Inequalities
Yayıncı	Element D.O.O.
Açık Erişim	Hayır
ISSN	1846-579X
E-ISSN	1846-579X
CiteScore	2,5
SJR	0,543
SNIP	0,825

THE STEIN-WEISS TYPE INEQUALITIES FOR THE B-RIESZ POTENTIALS

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