Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces

Authors : Cansu KESKİN, İsmail EKİNCİOĞLU

Pages : 1667-1675

Doi:10.15672/hujms.520995

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Publication Date : 2020-10-06

Article Type : Research Paper

Abstract :We prove the norm inequalities for potential operators and fractional integrals related to generalized shift operator defined on spaces of homogeneous type. We show that these operators are bounded from $H^{p}_{\Delta_{\nu}}$ to $H^{q}_{\Delta_{\nu}}$, for $\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{Q}$, provided $0<\alpha<\frac{1}{2}$, and $\alpha<\beta\leq 1$ and $\frac{Q}{Q+\beta} Keywords : Laplace Bessel operator, generalized shift operator, B n Riesz potential operator, atomic molecular decomposition, Hardy space

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