Riesz potential on weighted product Hardy spaces and inequalities

Key Points

• The aim is to explore the boundedness of the Riesz potential operator in weighted product Hardy spaces under specific conditions on the weight.
• Examined the Riesz potential operator with a focus on weights in Hardy spaces.
• Considered conditions where $rac{1}{p}- rac{1}{q} = rac{eta_1}{d_1} = rac{eta_2}{d_2}$.
• Analyzed boundedness from $H_w^{p}$ to $H_{w^{q/p}}^{q}$ and from $H_w^{p}$ to $L_{w^{q/p}}^{q}$.
• Proved that $I_eta$ is bounded from $L_w^{p}$ to $L_{w^{q/p}}^{q}$ under the specified weight conditions.
• Demonstrated the boundedness of $I_eta$ from $H_w^{p}$ to $H_{w^{q/p}}^{q}$.
• Verified similar properties for the maximal fractional operator in weighted Hardy spaces.