Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates
نویسندگان
چکیده
Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The authors then establish the duality between Hω,L(X ) and BMOρ,L(X ); as a corollary, the authors obtain the ρ-Carleson measure characterization of the space BMOρ,L(X ). Characterizations of Hω,L(X ), including the atomic and molecular characterizations and the Lusin area function characterization associated to the Poisson semigroup, are also presented. As applications, the authors obtain the characterizations of the Hardy spaces H L(R ) associated to the Schrödinger operator L = −∆+ V , where V ∈ L1loc (R) is a nonnegative potential and p ∈ (0, 1], in terms of the Lusin-area functions, the non-tangential maximal functions, the radial maximal functions, the atoms and the molecules. Finally, the authors show that the Riesz transform ∇L−1/2 is bounded from H L(R) to L(R) for all p ∈ (0, 1] and from H L(R) to the classical Hardy space H(R) for p ∈ ( n n+1 , 1]. All these results are new even when ω(t) = t for all t ∈ (0,∞) and p ∈ (0, 1).
منابع مشابه
Hankel Operators between Hardy-orlicz Spaces and Products of Holomorphic Functions
For Bn the unit ball of Cn, we consider Hardy-Orlicz spaces of holomorphic functions H, which are preduals of spaces of BMOA type with weight. We characterize the symbols of Hankel operators that extend into bounded operators from the Hardy-Orlicz H1 into H2 . We also consider the closely related question of integrability properties of the product of two functions, one in H1 and the other one i...
متن کاملp-Carleson Measures for a Class of Hardy-Orlicz Spaces
An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...
متن کاملRegularity in Orlicz spaces for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition∗
The purpose of this paper is to obtain the global regularity in Orlicz spaces for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition.
متن کاملNew Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators
We introduce a new class of Hardy spaces H(R), called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garćıa-Cuerva, Strömberg, and Torchinsky. Here, φ : R × [0,∞) → [0,∞) is a function such that φ(x, ·) is an Orlicz function and φ(·, t) is a MuckenhouptA∞ weight. A function f belongs to H(R) if and only if its maximal fu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009