一类全不连通群上的BMO和奇异积分算子(英文)

BMO and Singular Integrals over Certain Disconnected Groups

英文关键词:singular integral  BMO  weighted inequality.

中文摘要:

      本文主要讨论了定义在局部紧的全不连通群Ｇ上的一类卷积算子在加权Ｌ^∞（Ｇ）和ＢＭＯ（ａ）空间的性态．证明了如果卷积算子的核满足适当的条件，则算子是Ｌ^∞（Ｇ）到ＢＭＯ（ａ）有界的或是ＢＭＯ（ａ）到ＢＭＯ（ａ）有界的．

英文摘要:

      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).