BOUNDEDNESS OF HARDY TYPE OPERATORS ON Q-TYPE SPACES ASSOCIATED WITH WEIGHTS

Abstract

We investigate the boundedness of weight Hardy operators $U_{\psi }$ and the corresponding Cesàro type average operators $V_{\psi }$ on Q type spaces $Q_{\mathcal{𝒦},\lambda }^{p,q}({ℝ}^n)$. Moreover, we provide explicit norms for both $U_{\psi }$ and $V_{\psi }$ on $Q_{\mathcal{𝒦},\lambda }^{p,q}({ℝ}^n)$ under the assumption of the integrability of $\psi$.