Boundedness of homogeneous fractional integral operator on Morrey space

Abstract

For $0<\alpha<n$ , the homogeneous fractional integral operator $T_{\Omega,\alpha}$ is defined by $$T_{\Omega,\alpha}f(x)= \int_{{\Bbb {R}}^{n}}\frac{\Omega (x-y)}{\vert x-y\vert ^{n-\alpha}}f(y)\,dy. $$ In this paper we prove that if Ω satisfies some smoothness conditions on $S^{n-1}$ , then $T_{\Omega,\alpha}$ is bounded from $L^{\frac{\lambda}{\alpha },\lambda}({\Bbb {R}}^{n})$ to $\operatorname {BMO}({\Bbb {R}}^{n})$ , and from $L^{p,\lambda}({\Bbb {R}}^{n})$ ( $\frac{\lambda}{\alpha}< p<\infty$ ) to a class of the Campanato spaces $\mathcal{L}_{l,\lambda }({\Bbb {R}}^{n})$ , respectively.

Locations

• DOAJ (DOAJ: Directory of Open Access Journals) - View
• Journal of Inequalities and Applications - View - PDF