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

#### Cansu KESKİN [1] , İ̇smail EKİNCİOĞLU [2]

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.

Laplace-Bessel operator, generalized shift operator, $B_n$-Riesz potential operator, atomic-molecular decomposition, Hardy space
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-5636-1214Author: Cansu KESKİN (Primary Author)Institution: KÜTAHYA DUMLUPINAR ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİCountry: Turkey Orcid: 0000-0002-0998-4419Author: İ̇smail EKİNCİOĞLU Institution: KÜTAHYA DUMLUPINAR ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms520995, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1667 - 1675}, doi = {10.15672/hujms.520995}, title = {Some inequalities for homogeneous \$B\_n\$-potential type integrals on \$H\^\{p\}\_\{\\Delta\_\{\\nu\}\}\$ Hardy spaces}, key = {cite}, author = {Keski̇n, Cansu and Eki̇nci̇oğlu, İ̇smail} } APA Keski̇n, C , Eki̇nci̇oğlu, İ . (2020). Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1667-1675 . DOI: 10.15672/hujms.520995 MLA Keski̇n, C , Eki̇nci̇oğlu, İ . "Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1667-1675 Chicago Keski̇n, C , Eki̇nci̇oğlu, İ . "Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1667-1675 RIS TY - JOUR T1 - Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces AU - Cansu Keski̇n , İ̇smail Eki̇nci̇oğlu Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.520995 DO - 10.15672/hujms.520995 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1667 EP - 1675 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.520995 UR - https://doi.org/10.15672/hujms.520995 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces %A Cansu Keski̇n , İ̇smail Eki̇nci̇oğlu %T Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.520995 %U 10.15672/hujms.520995 ISNAD Keski̇n, Cansu , Eki̇nci̇oğlu, İ̇smail . "Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1667-1675 . https://doi.org/10.15672/hujms.520995 AMA Keski̇n C , Eki̇nci̇oğlu İ . Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1667-1675. Vancouver Keski̇n C , Eki̇nci̇oğlu İ . Some inequalities for homogeneous $B_n$-potential type integrals on $H^{p}_{\Delta_{\nu}}$ Hardy spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1667-1675.

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