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

Yıl 2020, Cilt: 49 Sayı: 5, 1667 - 1675, 06.10.2020

Cansu Keskin , İsmail Ekincioğlu

https://doi.org/10.15672/hujms.520995

Cited By: 1

Öz

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 $\frac{Q}{Q+\beta}<p\leq\frac{Q}{Q+\alpha}$. By applying atomic-molecular decomposition of $H^{p}_{\Delta_{\nu}}$ Hardy space, we obtain the boundedness of homogeneous fractional type integrals which extends the Stein-Weiss and Taibleson-Weiss's results for the boundedness of the $B_n$-Riesz potential operator on $H^{p}_{\Delta_{\nu}}$ Hardy space.

Anahtar Kelimeler

Laplace-Bessel operator, generalized shift operator, $B_n$-Riesz potential operator, atomic-molecular decomposition, Hardy space

Kaynakça

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