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Hall's transformation via quantum stochastic calculus

Paula Cohen, Robin Hudson, K. Parthasarathy, Sylvia Pulmannová (1998)

Banach Center Publications

It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make...

Hamilton’s Principle with Variable Order Fractional Derivatives

Atanackovic, Teodor, Pilipovic, Stevan (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation....

Hankel type operators on the unit disk

Jie Miao (2001)

Studia Mathematica

We study Hankel operators and commutators that are associated with a symbol and a kernel function. If the kernel function satisfies an upper bound condition, we obtain a sufficient condition for commutators to be bounded or compact. If the kernel function satisfies a local bound condition, the sufficient condition turns out to be necessary. The analytic and harmonic Bergman kernels satisfy both conditions, therefore a recent result by Wu on Hankel operators on harmonic Bergman spaces is extended....

Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

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 inequalities in function spaces

Hans Triebel (1999)

Mathematica Bohemica

Let Ω be a bounded C ∞ domain in ℝ n . The paper deals with inequalities of Hardy type related to the function spaces B p q s ( Ω ) and F p q s ( Ω ) .

Hardy Inequality in Variable Exponent Lebesgue Spaces

Diening, Lars, Samko, Stefan (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26D10, 46E30, 47B38We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.

Hardy space estimates for multilinear operators (I).

Ronald R. Coifman, Loukas Grafakos (1992)

Revista Matemática Iberoamericana

In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the Hp space context.

Hardy space estimates for multilinear operators (II).

Loukas Grafakos (1992)

Revista Matemática Iberoamericana

We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces Lp(Rn) into the Hardy spaces Hr(Rn). At the endpoint case r = n/(n + m + 1), where m is the highest vanishing moment of the multilinear operator, we prove a weak type result.

Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality.

Jacek Dziubanski, Jacek Zienkiewicz (1999)

Revista Matemática Iberoamericana

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 and the Dirichlet problem on Lipschitz domains.

Carlos E. Kenig, Jill Pipher (1987)

Revista Matemática Iberoamericana

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.

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