@article{article_520995, title={Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu }$ Hardy spaces}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={49}, pages={1667–1675}, year={2020}, DOI={10.15672/hujms.520995}, author={Keskin, Cansu and Ekincioğlu, İsmail}, keywords={Laplace-Bessel operator, generalized shift operator, $B_n$-Riesz potential operator, atomic-molecular decomposition, Hardy space}, abstract={<p>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 $\frac{Q}{Q+\beta}<p\leq\frac{Q}{Q+\alpha}$. <span style="font-size:12px;">  </span> <span style="font-size:12px;">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. </span> </p> <br />}, number={5}, publisher={Hacettepe University}