NORM INEQUALITY OF COMMUTATOR GENERATED BY THE FRACTIONAL INTEGRAL OPERATOR IN HARDY-AMALGAM SPACES WITH VARIABLE EXPONENTS $\mathrm{H}^{p(\cdot), q}(\mathrm{P})^d$
Keywords:
fractional integral operator, Hardy-amalgam spaces, variable exponent spaces, commutators, BMODOI:
https://doi.org/10.17654/0972111826003Abstract
Let $0<\gamma<d$ and $I_\gamma$ be the fractional integral operator of order $\gamma$ and we consider $\mathrm{P}^d$ the Euclidean space of dimension $d$. In this paper, we aim to prove some boundedness properties of commutator $\left[b, I_\gamma\right]$ generated by the fractional integral operator $I_\gamma$ and a suitable function $b$ on variable exponent spaces. Roughly speaking, we prove that the commutator $\left[b, I_\gamma\right]$ is extendable to a bounded linear operator from Hardy-amalgam spaces with variable exponents denoted $\mathrm{H}^{p(\cdot), q}\left(\mathrm{P}^d\right)$ to variable exponent amalgam spaces $\left(L^{p(\cdot)}, l^p\right)\left(\mathrm{P}^d\right)$ under appropriate conditions on the exponent $p(\cdot)$.
Received: September 14, 2025
Revised: November 7, 2025
Accepted: November 25, 2025
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