Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A o...Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.展开更多
The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L ...The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.展开更多
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.
基金Supported in part by National and Zhejiang Provincial Natural Science Foundations of China.Partof the work contained in this paper was done while the second named author was visiting Simon Fraser University,Canada,he thanks Dr.P.B.Borwein and the Depa
文摘The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
