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

Abstract

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 $ {1 \over q(z)} = {1 \over p(z)}-{\zeta (z) \over n} $ when $ p(z) $ is not necessarily constant at infinity.

Keywords

• lebesgue spaces
• weighted estimates
• hardy operators
• grand herz spaces