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	The partial derivative-problem for multipliers of the Sobolev space
	Xiao, J
	1998
关键词	DIRICHLET SPACE ANALYTIC-FUNCTIONS BESOV-SPACES INTERPOLATION
英文摘要	For alpha is an element of (0, 1/2], let M(L-alpha(2)) and M(D-alpha) be the spaces of multipliers of L-alpha(2), the Sobolev space on the unit circle, and D-alpha, the Dirichlet type space on the open unit disk, respectively. In fact, M(D-alpha) and D-alpha are obtained from M(L-alpha(2)) and L-alpha(2) by analytic extension. In this paper, we show that if \g(z)\(2)(1 - \z\(2))(1-2 alpha) dm(z) is an alpha-Carleson measure on the open unit disk, then there exists a function f defined on the closed unit disk such that the equation partial derivative f/partial derivative (z) over bar = g(z) holds on the open unit disk, and such that the boundary value function f belongs to M(L-alpha(2)). For applications, we first establish the corona theorem for M(D-alpha), which, in the case alpha = 1/2, gives the answer to a question of L. Brown and A. L. Shields. Secondly, we obtain a geometric characterization of the interpolating sequences for M(D alpha) with alpha is an element of (0, 1/2) that extends a theorem of D. E. Marshall and C. Sundberg.; Mathematics; SCI(E); 9; ARTICLE; 2; 217-232; 97
语种	英语
出处	SCI
出版者	manuscripta mathematica
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/158057]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xiao, J. The partial derivative-problem for multipliers of the Sobolev space. 1998-01-01.

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