From Weak to Strong L 1 -convergence by an Oscillation Restriction Criterion of Bmo Type
نویسنده
چکیده
Recently, Girardi gave a characterization of relative strong L 1 R-compactness in terms of relative weak L 1 R-compactness and the Bocce criterion 18]. Here this result is generalized and extended by presenting a less stringent oscillation restriction condition (ORC) which enforces the transcendence of weak into an appropiately reformulated form of strong convergence in L 1 E , for E a separable reeexive Banach space. The proof has a very simple, transparent structure, because it relies on basic, well-known facts from Young measure theory; this brings the result in line with the current literature.
منابع مشابه
Hardy Spaces, Commutators of Singular Integral Operators Related to Schrödinger Operators and Applications
Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...
متن کاملStrong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings
In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...
متن کاملCompactness in L 1 , D - P Operators , Geometry of Banach Spaces
A type of oscillation modeled on BMO is introduced to characterize norm compactness in L 1. This result is used to characterize the bounded linear operators from L 1 into a Banach space X that map weakly convergent sequences onto norm convergent sequences (i.e. are Dunford-Pettis). This characterization is used to study the geometry of Banach spaces X with the property that all bounded linear o...
متن کاملToeplitz Operators with Bmo Symbols on the Segal-bargmann Space
We show that Zorboska’s criterion for compactness of Toeplitz operators with BMO symbols on the Bergman space of the unit disc holds, by a different proof, for the Segal-Bargmann space of Gaussian square-integrable entire functions on Cn. We establish some basic properties of BMO for p ≥ 1 and complete the characterization of bounded and compact Toeplitz operators with BMO symbols. Via the Barg...
متن کاملSampling and Reconstruction of Bandlimited BMO-Functions
Functions of bounded mean oscillation (BMO) play an important role in complex function theory and harmonic analysis. In this paper a sampling theorem for bandlimited BMO-functions is derived for sampling points that are the zero sequence of some sine-type function. The class of sinetype functions is large and, in particular, contains the sine function, which corresponds to the special case of e...
متن کامل