A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent

Abstract

<abstract><p>The fractional Hardy-type operators of variable order is shown to be bounded from the grand Herz spaces $ {\dot{K} ^{a(\cdot), u), \theta}_{ p(\cdot)}(\mathbb{R}^n)} $ with variable exponent into the weighted space $ {\dot{K} ^{a(\cdot), u), \theta}_{\rho, q(\cdot)}(\mathbb{R}^n)} $, where $ \rho = (1+|z_1|)^{-\lambda} $ and</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ {1 \over q(z)} = {1 \over p(z)}-{\zeta (z) \over n} $\end{document} </tex-math></disp-formula></p> <p>when $ p(z) $ is not necessarily constant at infinity.</p></abstract>