Abstract
Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a \(C^1\)-function on \({\mathbb R}^N{\setminus } \{0\}\) which vanishes outside the unit ball.
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Maeda, FY., Mizuta, Y. & Shimomura, T. Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball. Collect. Math. 69, 377–394 (2018). https://doi.org/10.1007/s13348-017-0210-x
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DOI: https://doi.org/10.1007/s13348-017-0210-x
Keywords
- Weighted norm inequality
- Variable exponent
- Sobolev’s inequality
- Riesz potentials
- Sobolev integral representation