Commutants of certain multiplication operators on Hilbert spaces of analytic functions

K. Seddighi; S. Vaezpour

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Displaying similar documents to “Commutants of certain multiplication operators on Hilbert spaces of analytic functions”

Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Christopher Boyd (1993)

Studia Mathematica

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For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that $G {(U)}_{i}^{'} = (ℋ (U), τ_{δ})$ . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the $τ_{0}$ and $τ_{ω}$ topologies on ℋ (U).

A new Taylor type formula and $C^{\infty}$ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

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The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have $C^{\infty}$ extensions from any subpolysector; the Gevrey case is included.

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group

Silvia Secco (1999)

Studia Mathematica

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$L^{p}$ - $L^{q}$ boundedness properties are obtained for operators defined by convolution with measures supported on certain curves on the Heisenberg group. We find the curvature condition for which the type set of these operators can be the full optimal trapezoid with vertices A=(0,0), B=(1,1), C=(2/3,1/2), D=(1/2,1/3). We also give notions of right curvature and left curvature which are not mutually equivalent.

Integral operators and weighted amalgams

C. Carton-Lebrun, H. Heinig, S. Hofmann (1994)

Studia Mathematica

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For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from $ℓ^{q ̅} (L_{v}^{p ̅})$ into $ℓ^{q} (L_{u}^{p})$ . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted $L^{p}$ -spaces. Amalgams of the form $ℓ^{q} (L_{w}^{p})$ , 1 < p,q < ∞ , q ≠ p, $w \in A_{p}$ , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.

Oscillatory kernels in certain Hardy-type spaces

Lung-Kee Chen, Dashan Fan (1994)

Studia Mathematica

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We consider a convolution operator Tf = p.v. Ω ⁎ f with $Ω (x) = K (x) e^{i h (x)}$ , where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued $C^{\infty}$ function on $ℝ^{n} ∖ 0$ . We give a criterion for such an operator to be bounded from the space $H_{0}^{p} (ℝ^{n})$ into itself.

Representations of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

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We give a representation of the spaces $C^{\infty} (ℝ^{N}) \cap H^{k, p} (ℝ^{N})$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^{\infty} (ℝ^{N}) \cap H^{k, 2} (ℝ^{N})$ is isomorphic to the sequence space $s^{ℕ} \cap l^{2} (l^{2})$ , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

$B M O_{ψ}$ -spaces and applications to extrapolation theory

Stefan Geiss (1997)

Studia Mathematica

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We investigate a scale of $B M O_{ψ}$ -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with $B M O_{ψ}$ - $L_{\infty}$ -estimates, and arrives at $L_{p}$ - $L_{p}$ -estimates, or more generally, at estimates between K-functionals from interpolation theory.

Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm

A. Pełczyński, M. Wojciechowski (1993)

Studia Mathematica

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Let E be a Banach space. Let $L ¹_{(1)} (ℝ^{d}, E)$ be the Sobolev space of E-valued functions on $ℝ^{d}$ with the norm $ʃ_{ℝ^{d}} ∥ f ∥_{E} d x + ʃ_{ℝ^{d}} ∥ \nabla f ∥_{E} d x = ∥ f ∥ ₁ + ∥ \nabla f ∥ ₁$ . It is proved that if $f \in L ¹_{(1)} (ℝ^{d}, E)$ then there exists a sequence $(g_{m}) \subset L_{(1)} ¹ (ℝ^{d}, E)$ such that $f = \sum_{m} g_{m}$ ; $\sum_{m} (∥ g_{m} ∥ ₁ + ∥ \nabla g_{m} ∥ ₁) < \infty$ ; and $∥ g_{m} ∥_{\infty}^{1 / d} ∥ g_{m} ∥ ₁^{(d - 1) / d} \leq b ∥ \nabla g_{m} ∥ ₁$ for m = 1, 2,..., where b is an absolute constant independent of f and E. The result is applied to prove various refinements of the Sobolev type embedding $L_{(1)} ¹ (ℝ^{d}, E) ↪ L ² (ℝ^{d}, E)$ . In particular, the embedding into Besov spaces $L ¹_{(1)} (ℝ^{d}, E) ↪ B_{p, 1}^{θ (p, d)} (ℝ^{d}, E)$ is proved, where $θ (p, d) = d (p^{- 1} + d^{- 1} - 1)$ for 1 < p ≤ d/(d-1), d=1,2,... The latter embedding in the scalar case is due to Bourgain...

A characterization of some weighted norm inequalities for the fractional maximal function

Richard Wheeden (1993)

Studia Mathematica

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A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L_{v}^{p} (X)$ to $L_{w}^{q} (X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.

Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves

Tao Qian (1997)

Studia Mathematica

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The paper presents a theory of Fourier transforms of bounded holomorphic functions defined in sectors. The theory is then used to study singular integral operators on star-shaped Lipschitz curves, which extends the result of Coifman-McIntosh-Meyer on the $L^{2}$ -boundedness of the Cauchy integral operator on Lipschitz curves. The operator theory has a counterpart in Fourier multiplier theory, as well as a counterpart in functional calculus of the differential operator 1/i d/dz on the curves. ...

Holomorphic motions commuting with semigroups

Zbigniew Słodkowski (1996)

Studia Mathematica

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A holomorphic family $f_{z}$ , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_{z}$ , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_{z}$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ ̅ ̅ ̅ ̅ ̅ ̅ f_{z} (E)$ , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed. ...

Singularities of triples of vector fields on $R^{4}$ : the focusing stratum

Piotr Mormul (1988)

Studia Mathematica

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Moment inequalities for sums of certain independent symmetric random variables

P. Hitczenko, S. Montgomery-Smith, K. Oleszkiewicz (1997)

Studia Mathematica

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This paper gives upper and lower bounds for moments of sums of independent random variables $(X_{k})$ which satisfy the condition ${P (| X |}_{k} \geq t) = e x p (- N_{k} (t))$ , where $N_{k}$ are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which $N (t) = {| t |}^{r}$ for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N.

On joint spectra of pairs of analytic Toeplitz operators

Mihai Putinar (1995)

Studia Mathematica

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One computes the joint and essential joint spectra of a pair of multiplication operators with bounded analytic functions on the Hardy spaces of the unit ball in $ℂ^{n}$ .