BMO and Singular Integrals over Certain Disconnected Groups

Abstract:

      In this paper the authors study proprieties of certain convolution operators on L^∞ (G) and weighted BMO(a)(G) spaces,where G is a locally compact totally disconnected group with a suitable sequence of open compact subgroups. The authors prove that if the kernel satisfies certain conditions, then the convolution operator is bounded from L^∞ to BMO(a) or from BMO(a) to BMO(ａ).