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

Autor: Samia Bashir, Babar Sultan, Amjad Hussain, Aziz Khan, Thabet Abdeljawad
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: AIMS Mathematics, Vol 8, Iss 9, Pp 22178-22191 (2023)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.20231130?viewType=HTML
Popis: 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.
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