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Displaying similar documents to “On H ˇ n -bubbles in n-dimensional compacta”

A lifting theorem for locally convex subspaces of L 0

R. Faber (1995)

Studia Mathematica

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We prove that for every closed locally convex subspace E of L 0 and for any continuous linear operator T from L 0 to L 0 / E there is a continuous linear operator S from L 0 to L 0 such that T = QS where Q is the quotient map from L 0 to L 0 / E .

On the complemented subspaces of the Schreier spaces

I. Gasparis, D. Leung (2000)

Studia Mathematica

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It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space X ξ generated by subsequences ( e l n ξ ) and ( e m n ξ ) , respectively, of the natural Schauder basis ( e n ξ ) of X ξ are isomorphic if and only if ( e l n ξ ) and ( e m n ξ ) are equivalent. Further, X ξ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of ( e n ξ ) . It is also shown that there exists a complemented subspace spanned by a block basis of ( e n ξ ) , which is not isomorphic to a subspace generated by a subsequence of ( e n ζ ) ,...

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

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Let m: ℝ → ℝ be a function of bounded variation. We prove the L p ( ) -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by T m f ( x ) = p . v . k ( x - y ) m ( x + y ) f ( y ) d y where k ( x ) = j 2 j φ j ( 2 j x ) for a family of functions φ j j satisfying conditions (1.1)-(1.3) given below.

Nonconvolution transforms with oscillating kernels that map 1 0 , 1 into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form ( Ω f ) ( y ) = ʃ - Ω ( y , u ) f ( u ) d u with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and h L (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space 1 0 , 1 (= B) into itself. In particular, all operators with h ( y ) = e i | y | a , a > 0, a ≠ 1, map B into itself.

On invariant measures for power bounded positive operators

Ryotaro Sato (1996)

Studia Mathematica

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We give a counterexample showing that ( I - T * ) L ¯ L + = 0 does not imply the existence of a strictly positive function u in L 1 with Tu = u, where T is a power bounded positive linear operator on L 1 of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.

Tauberian theorems for Cesàro summable double sequences

Ferenc Móricz (1994)

Studia Mathematica

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( s j k : j , k = 0 , 1 , . . . ) be a double sequence of real numbers which is summable (C,1,1) to a finite limit. We give necessary and sufficient conditions under which ( s j k ) converges in Pringsheim’s sense. These conditions are satisfied if ( s j k ) is slowly decreasing in certain senses defined in this paper. Among other things we deduce the following Tauberian theorem of Landau and Hardy type: If ( s j k ) is summable (C,1,1) to a finite limit and there exist constants n 1 > 0 and H such that j k ( s j k - s j - 1 , k - s j - 1 , k + s j - 1 , k - 1 ) - H , j ( s j k - s j - 1 , k ) - H and k ( s j k - s j , k - 1 ) - H whenever j , k > n 1 , then...

On the representation of functions by orthogonal series in weighted L p spaces

M. Grigorian (1999)

Studia Mathematica

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It is proved that if φ n is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form k = 1 c k φ k ( x ) , where c k l q for all q>2, with the following properties: 1. For any p ∈ [1,2) and f L μ p [ 0 , 1 ] = f : ʃ 0 1 | f ( x ) | p μ ( x ) d x < there are numbers ɛ k , k=1,2,…, ɛ k = 1 or 0, such that l i m n ʃ 0 1 | k = 1 n ɛ k c k φ k ( x ) - f ( x ) | p μ ( x ) d x = 0 . 2. For every p ∈ [1,2) and f L μ p [ 0 , 1 ] there are a function g L 1 [ 0 , 1 ] with g(x) = f(x) on E and numbers δ k , k=1,2,…, δ k = 1 or 0,...

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

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C. Watari [12] obtained a simple characterization of Lipschitz classes L i p ( p ) α ( W ) ( 1 p , α > 0 ) on the dyadic group using the L p -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces B p , q α on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces B p , q α by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system

G. Gát (1998)

Studia Mathematica

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Let G be the Walsh group. For f L 1 ( G ) we prove the a. e. convergence σf → f(n → ∞), where σ n is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator σ * f s u p n | σ n f | . We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, σ * f 1 c | f | H , where H is the Hardy space on the Walsh group.

Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

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Let s* denote the maximal function associated with the rectangular partial sums s m n ( x , y ) of a given double function series with coefficients c j k . The following generalized Hardy-Littlewood inequality is investigated: | | s * | | p , μ C p , α , β Σ j = 0 Σ k = 0 ( j ̅ ) p - α - 2 ( k ̅ ) p - β - 2 | c j k | p 1 / p , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on c j k and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property...

The local versions of H p ( n ) spaces at the origin

Shan Lu, Da Yang (1995)

Studia Mathematica

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Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces H K ̇ q α , p ( n ) which are the local versions of H p ( n ) spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth’s sense. We also prove an interpolation theorem for operators on H K ̇ q α , p ( n ) and discuss the H K ̇ q α , p ( n ) -boundedness of Calderón-Zygmund operators. Similar results can also be obtained...