Multipliers on Dirichlet Type Spaces |
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| Authors: | Peng Yan Hu Ji Huai Shi |
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| Institution: | (1) Department of Mathematics, Normal College of Shenzhen University, Shenzhen, Guangdong 518060, P. R. China;(2) Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China |
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| Abstract: | In this paper, we characterize the pointwise multiplier space M (D
τ, D
μ) of Dirichlet type spaces in the unit ball of C
n
for the values of τ, μ in three cases: (i) τ < 0,μ < 0, (ii) τ < μ, (iii) τ≥μ, τ > n, and construct two functions to show that M(D
τ) ⊂D
τ properly if τ≤n and M(D
τ) ⊂M(D
μ) properly if τ > μ and τ > n− 1.
Supported by the National Natural Science Foundation of China and the National Education Committee Doctoral
Foundation of China |
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| Keywords: | Dirichlet space Pointwise multiplier Holomorphic function |
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