Noncommutative extrapolation theorems and applications
نویسندگان
چکیده
منابع مشابه
Two Extrapolation Theorems for Related Weights and Applications
In this paper we prove two extrapolation theorems for related weights. The theorems proved by C. Segovia and J.L. Torrea in [C. Segovia and J.L. Torrea, Weighted inequalities for commutators of fractional and singular integrals. Publ. Mat. 35 (1991) 209-235] are adapted for one-sided weights. We apply these extrapolation theorems to improve weighted inequalities for commutators (with symbol b d...
متن کاملNoncommutative Maximal Ergodic Theorems
The connection between ergodic theory and the theory of von Neumann algebras goes back to the very beginning of the theory of “rings of operators”. Maximal inequalities in ergodic theory provide an important tool in classical analysis. In this paper we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic theorem, thereby connecting these different aspects of ergod...
متن کاملThe Noncommutative Hahn-banach Theorems
The Hahn-Banach theorem in its simplest form asserts that a bounded linear functional defined on a subspace of a Banach space can be extended to a linear functional defined everywhere, without increasing its norm. There is an order-theoretic version of this extension theorem (Theorem 0.1 below) that is often more useful in context. The purpose of these lecture notes is to discuss the noncommuta...
متن کاملOn Noncommutative Weighted Local Ergodic Theorems
In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ , and {αt} a strongly continuous extension to L(M, τ ) of a semigroup of absolute contractions on L(M, τ ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ∈ L(M, τ ), the averages 1 T Z T 0 b(t)αt(x)dt converge bilateral almost uniform in L(M, τ ) as T ...
متن کاملRelative volume comparison theorems in Finsler geometry and their applications
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2009
ISSN: 0019-2082
DOI: 10.1215/ijm/1266934788