Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels
Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels
We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and its commutator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">[</mml:mo><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo></mml:math> on Morrey-Herz space with …