Hardy’s inequalities and integral operators on Herz-Morrey spaces

Abstract

We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.

Keywords

• herz spaces
• morrey spaces
• central morrey space
• hardy’s inequalities
• integral operators
• boyd’s indices
• hadamard fractional integrals
• hilbert inequality
• 42b35
• 44a15
• 46e30