Generalized fractional integrals on central Morrey spaces and generalized $\lambda$-CMO spaces
Volume 102 / 2014
Banach Center Publications 102 (2014), 181-188
MSC: Primary 42B35; Secondary 26A33, 46E30, 46E35.
DOI: 10.4064/bc102-0-12
Abstract
We introduce the generalized fractional integrals ${\tilde{I}}_{\alpha,d}$ and prove the strong and weak boundedness of ${\tilde{I}}_{\alpha,d}$ on the central Morrey spaces $B^{p,\lambda}(\mathbb R^n)$. In order to show the boundedness, the generalized $\lambda$-central mean oscillation spaces $\Lambda^{(d)}_{p,\lambda}(\mathbb R^n)$ and the generalized weak $\lambda$-central mean oscillation spaces $W\Lambda^{(d)}_{p,\lambda}(\mathbb R^n)$ play an important role.
