, bmo, blo and Littlewood-Paley -functions with non-doubling measures.
-BMO duality on graphs
On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.
spaces associated with Schrödinger operators with potentials from reverse Hölder classes
Let A = -Δ + V be a Schrödinger operator on , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of if the maximal function belongs to , where is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space admits a special atomic decomposition.
spaces over open subsets of
H¹ and BMO for certain locally doubling metric measure spaces of finite measure
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...
Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications
Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable...
Hardy and Lipschitz spaces on subsets of
Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality.
Let {Tt}t>0 be the semigroup of linear operators generated by a Schrödinger operator -A = Δ - V, where V is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space HA1 by means of a maximal function associated with the semigroup {Tt}t>0. Atomic and Riesz transforms characterizations of HA1 are shown.
Hardy spaces, A..., and singular integrals on chord-arc domains
Hardy spaces and oscillatory singular integrals.
Hardy spaces and the Dirichlet problem on Lipschitz domains.
Our concern in this paper is to describe a class of Hardy spaces Hp(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ Rn when n ≥ 3, and a certain smooth counterpart of Hp(D) on Rn-1, by providing an atomic decomposition and a description of their duals.
Hardy spaces associated with some Schrödinger operators
For a Schrödinger operator A = -Δ + V, where V is a nonnegative polynomial, we define a Hardy space associated with A. An atomic characterization of is shown.
Hardy spaces H¹ for Schrödinger operators with certain potentials
Let be the semigroup of linear operators generated by a Schrödinger operator -L = Δ - V with V ≥ 0. We say that f belongs to if . We state conditions on V and which allow us to give an atomic characterization of the space .
Hardy spaces of conjugate temperatures
We define Hardy spaces of pairs of conjugate temperatures on using the equations introduced by Kochneff and Sagher. As in the holomorphic case, the Hilbert transform relates both components. We demonstrate that the boundary distributions of our Hardy spaces of conjugate temperatures coincide with the boundary distributions of Hardy spaces of holomorphic functions.
Hardy spaces on compact Lie groups
Hardy spaces on SU(2)
Hardy Spaces on the Plane and Double Fourier Transforms.
Hardy's inequality for compact Lie groups.
Hardy-type inequalities for Hermite expansions.
Hardy-type inequalities on the real line.