Tent Spaces associated with Semigroups of Operators
نویسنده
چکیده
We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO duality theory. We also get a H1-BMO duality inequality without assuming the monotone property. All the results are proved in a more general setting, namely for noncommutative Lp spaces.
منابع مشابه
Tent Spaces Associated with Markov Semigroups
0 Ts|Bt| dt t ) 1 2 ||L∞(Ω). for any family (At)t≥0 ∈ L(Ω, μ), (Bt)t≥0 ∈ L∞(Ω, μ) provided (Tt)t≥0 does not increase or decrease “too fast”. As an application, we prove a duality inequality for H − BMO spaces associated with general subordinated Poisson semigroups. All the results are proved in a more general setting, that is for (Bt)t≥0 and (At)t≥0 being families of elements of a semifinte von...
متن کاملSemigroups and Stability of Nonautonomous Differential Equations in Banach Spaces
This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators ...
متن کاملHardy Spaces Associated with Semigroups of Operators
This paper is a non exhaustive survey about Hardy spaces defined by semigroups of operators.
متن کاملOn Two-parameter Dynamical Systems and Applications
In this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on Banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed
متن کاملOn a Theorem of Zabczyk for Semigroups of Operators in Locally Convex Spaces
The purpose of this paper is to extend a stability theorem of Zabczyk to the case of semigroups of operators in locally convex topological vector spaces. Obtained results generalize the similar theorems proved by Datko, Pazy, Rolewicz and Littman for the case of C0-semigroups of operators in Banach spaces. AMS Mathematics Subject Classification (2000): 34D05,34D20
متن کامل