is a Grothendieck space
Hankel forms
It is an open question whether Nehari's theorem on the circle group has an analogue on the infinite-dimensional torus. In this note it is shown that if the analogue holds, then some interesting inequalities follow for certain trigonometric polynomials on the torus. We think these inequalities are false but are not able to prove that.
Hankel forms and the Fock space.
Hankel multipliers and transplantation operators
Connections between Hankel transforms of different order for -functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.
Hankel operators and the Dixmier trace on strictly pseudoconvex domains.
Hankel operators and weak factorization for Hardy-Orlicz spaces
We study the holomorphic Hardy-Orlicz spaces , where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in ℂⁿ. The function Φ is in particular such that for some p > 0. We develop maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Ω). As a consequence, we characterize those Hankel operators which are bounded from into ¹(Ω).
Hankel Operators on Bergman Spaces with Change of Weight.
Hankel type operators on the unit disk
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....
Ha-Plitz Operators between Moebius Invariant Subspaces.
Hardy Inequality in Variable Exponent Lebesgue Spaces
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).
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).
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.
Harmonic analysis on the quantized Riemann sphere.
Harmonic Bergman spaces with small exponents in the unit ball.
Hausdorff Matrices as Bounded Operators over lp.
Hereditarily finitely decomposable Banach spaces
A Banach space is said to be if the maximal number of subspaces of X forming a direct sum is finite and equal to n. We study some properties of spaces, and their links with hereditarily indecomposable spaces; in particular, we show that if X is complex , then dim , where S(X) denotes the space of strictly singular operators on X. It follows that if X is a real hereditarily indecomposable space, then ℒ(X)/S(X) is a division ring isomorphic either to ℝ, ℂ, or ℍ, the quaternionic division ring....
Hermitian composition operators on Hardy-Smirnov spaces
Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
Hermitian Operators on C (X, E) and the Banach-Stone Theorem.
Hidden symmetry from supersymmetry in one-dimensional quantum mechanics.
Hilbert inequality for vector valued functions
In this paper we consider a class of Hankel operators with operator valued symbols on the Hardy space where is a separable infinite dimensional Hilbert space and showed that these operators are unitarily equivalent to a class of integral operators in We then obtained a generalization of Hilbert inequality for vector valued functions. In the continuous case the corresponding integral operator has matrix valued kernels and in the discrete case the sum involves inner product of vectors in the...