Displaying similar documents to “Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces”

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 function on n 0 . We give a criterion for such an operator to be bounded from the space H 0 p ( n ) into itself.

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 q ̅ ( L v p ̅ ) into 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 q ( L w p ) , 1 < p,q < ∞ , q ≠ p, w 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.

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 ) ( d , E ) be the Sobolev space of E-valued functions on d with the norm ʃ d f E d x + ʃ d f E d x = f + f . It is proved that if f L ¹ ( 1 ) ( d , E ) then there exists a sequence ( g m ) L ( 1 ) ¹ ( d , E ) such that f = m g m ; m ( g m + g m ) < ; and g m 1 / d g m ( d - 1 ) / d b g m 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 ( d , E ) L ² ( d , E ) . In particular, the embedding into Besov spaces L ¹ ( 1 ) ( d , E ) B p , 1 θ ( p , d ) ( 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 new Taylor type formula and C 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 extensions from any subpolysector; the Gevrey case is included.

Commutants of certain multiplication operators on Hilbert spaces of analytic functions

K. Seddighi, S. Vaezpour (1999)

Studia Mathematica

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This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let A = M z be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with A n for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.

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.

Representations of the spaces C ( N ) H k , p ( N )

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

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We give a representation of the spaces C ( N ) H k , p ( 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 ( N ) H k , 2 ( N ) is isomorphic to the sequence space s l 2 ( l 2 ) , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

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 ̅ ̅ ̅ ̅ ̅ ̅ f z ( E ) , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed. ...

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 -estimates, and arrives at L p - L p -estimates, or more generally, at estimates between K-functionals from interpolation theory.

Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis

Paolo Terenzi (1994)

Studia Mathematica

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Every separable, infinite-dimensional Banach space X has a biorthogonal sequence z n , z * n , with s p a n z * n norming on X and z n + z * n bounded, so that, for every x in X and x* in X*, there exists a permutation π(n) of n so that x c o n v ¯ f i n i t e s u b s e r i e s o f n = 1 z * n ( x ) z n a n d x * n ( x ) = n = 1 z * π ( n ) ( x ) x * ( z π ( n ) ) .

Uniqueness of complete norms for quotients of Banach function algebras

W. Bade, H. Dales (1993)

Studia Mathematica

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We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra L 1 ( G ) of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients A ( Γ ) / J ( E ) ¯ arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed....

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.

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 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 the size of approximately convex sets in normed spaces

S. Dilworth, Ralph Howard, James Roberts (2000)

Studia Mathematica

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Let X be a normed space. A set A ⊆ X is approximately convexif d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with ( A , C o ( A ) ) l o g 2 n - 1 and d i a m ( A ) C n ( l n n ) 2 , where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.

Subanalytic version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (1997)

Studia Mathematica

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For any subanalytic C k -Whitney field (k finite), we construct its subanalytic C k -extension to n . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.

Comparing gaussian and Rademacher cotype for operators on the space of continuous functions

Marius Junge (1996)

Studia Mathematica

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We prove an abstract comparison principle which translates gaussian cotype into Rademacher cotype conditions and vice versa. More precisely, let 2 < q < ∞ and T: C(K) → F a continuous linear operator. (1) T is of gaussian cotype q if and only if ( k ( ( T x k F ) / ( l o g ( k + 1 ) ) ) q ) 1 / q c k ɛ k x k L 2 ( C ( K ) ) , for all sequences ( x k ) k C ( K ) with ( T x k ) k = 1 n decreasing. (2) T is of Rademacher cotype q if and only if ( k ( T x k F ( ( l o g ( k + 1 ) ) q ) ) 1 / q c k g k x k L 2 ( C ( K ) ) , for all sequences ( x k ) k C ( K ) with ( T x k ) k = 1 n decreasing. Our method allows a restriction to a fixed number of vectors and complements the corresponding results of...