We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz trans...We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, CalderSn-Zygmund operators for all possible values of type parameter λ, in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.展开更多
Abstract In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fs,w p,q （Rn） with local weight w by using the Lusin-area functions for the full ranges of the indices, and then establish ...Abstract In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fs,w p,q （Rn） with local weight w by using the Lusin-area functions for the full ranges of the indices, and then establish their atomic decompositions for s ∈ R, p ∈ （0, 1] and q ∈ [p, ∞）. The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in （0, 1]. Finite atomic decompositions for smooth functions in Fs,w p,q（Rn） are also obtained, which further implies that a （sub）linear operator that maps smooth atoms of Fs,w p,q（Rn） uniformly into a bounded set of a （quasi-）Banach space is extended to a bounded operator on the whole Fs,w p,q（Rn） As an application, the baundedness of the local Riesz operator on the space Fs,w p,q（Rn） is obtained.展开更多
基金supported by MTM2010/17974an FPU Grant from the Government of Spain
文摘We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, CalderSn-Zygmund operators for all possible values of type parameter λ, in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.
基金supported by the National Natural Science Foundation of China(Nos.11101425,11171027)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20120003110003)
文摘Abstract In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fs,w p,q （Rn） with local weight w by using the Lusin-area functions for the full ranges of the indices, and then establish their atomic decompositions for s ∈ R, p ∈ （0, 1] and q ∈ [p, ∞）. The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in （0, 1]. Finite atomic decompositions for smooth functions in Fs,w p,q（Rn） are also obtained, which further implies that a （sub）linear operator that maps smooth atoms of Fs,w p,q（Rn） uniformly into a bounded set of a （quasi-）Banach space is extended to a bounded operator on the whole Fs,w p,q（Rn） As an application, the baundedness of the local Riesz operator on the space Fs,w p,q（Rn） is obtained.
