Abstract In this paper, we first prove that, for a non-zero function f∈D（Rn）, its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D＇H（Rn） is constr...Abstract In this paper, we first prove that, for a non-zero function f∈D（Rn）, its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D＇H（Rn） is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D’H（Rn） is the biggest subspace of D＇（Rn） on which the extended multi-Hilbert transform is a homeomorphism.展开更多
基金Supported by the National Natural Science Foundation of China (No: 11471309 11271162+2 种基金 11561062)the Nanhu Scholar Program for Young Scholars of XYNUDoctoral Scientific Research Startup Fund of Xinyang Normal University (2016)
文摘Abstract In this paper, we first prove that, for a non-zero function f∈D（Rn）, its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D＇H（Rn） is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D’H（Rn） is the biggest subspace of D＇（Rn） on which the extended multi-Hilbert transform is a homeomorphism.
