Fractional operators with homogeneous kernels in weighted Herz spaces with variable exponent

Abstract

Let $\mathrm{\Omega }\in L^s\left({\mathbb{S}}^{n-1}\right)$, with $s\ge 1$, be a homogeneous function of degree zero. In this paper, we establish the boundedness of the homogeneous fractional integral operator on weighted Herz spaces with variable exponent ${\dot{K}}_{p(\cdot )}^{\alpha ,q}\left(w\right)$.

COMMUNICATED BY:

• M. A. Ragusa

Keywords:

• Fractional integral
• homogeneous kernel
• Muckenhoupt
• weighted Herz space
• variable exponent

2010 Mathematics Subject Classifications:

• 42B20
• 42B25

Disclosure statement

No potential conflict of interest was reported by the author(s).