Results 1 to 10 of about 34,122 (124)
A Hausdorff-Young theorem for rearrangement-invariant spaces [PDF]
Pacific Journal of Mathematics, 1973 The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1
Bennett, Colin
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Cones generated by a generalized fractional maximal function [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The paper considers the space of generalized fractional-maximal function, constructed on the basis of a rearrangement-invariant space. Two types of cones generated by a nonincreasing rearrangement of a generalized fractional-maximal function and
N.А. Bokayev +2 more
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Subspaces of Rearrangement-Invariant Spaces [PDF]
Canadian Journal of Mathematics, 1996 AbstractWe prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, ∞) which is p-convex for some p > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice.
Hernandez, Francisco L. +1 more
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SURJECTIVE ISOMETRIES ON REARRANGEMENT-INVARIANT SPACES [PDF]
The Quarterly Journal of Mathematics, 1994 We prove that if $X$ is a real rearrangement-invariant function space on $[0,1]$, which is not isometrically isomorphic to $L_2,$ then every surjective isometry $T:X\to X$ is of the form $Tf(s)=a(s)f( (s))$ for a Borel function $a$ and an invertible Borel map $ :[0,1] \to [0,1].$ If $X$ is not equal to $L_p$, up to renorming, for some $1\le p\le ...
Kalton, N. J., Randrianantoanina, Beata
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On boundedness of the Hilbert transform on Marcinkiewicz spaces
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 We study boundedness properties of the classical (singular) Hilbert transform (Hf)(t) = p.v.1/π ∫R f(s)/(t − s) ds, acting on Marcinkiewicz spaces. The Hilbert transform is a linear operator which arises from the study of boundary values of the real and
N.T. Bekbayev, K.S. Tulenov
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Advanced Nonlinear Studies, 2021 Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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Factorization property in rearrangement invariant spaces
Advances in Operator Theory, 2023 Let $X$ be a Banach space with a basis $(e_k)_k$ and biorthogonals $(e^\ast_k)_k$. An operator on $X$ is said to have a $\textit {large diagonal}$ if $\inf\limits_{k} |e_k^\ast(T(e_k))| > 0$. The basis $(e_k)_k$ is said to have the $\textit {factorization property}$ if the identity factors through any operator with a large diagonal.
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Weak-type boundedness of the Fourier transform on rearrangement invariant function spacest [PDF]
, 2018 We study several questions about the weak-type boundedness of the Fourier transform F on rearrangement invariant spaces. In particular, we characterize the action of F as a bounded operator from the minimal Lorentz space ¿(X) into the Marcinkiewicz ...
Boza Rocho, Santiago +1 more
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Lushness, numerical index 1 and the Daugavet property in rearrangement invariant spaces [PDF]
, 2011 We show that for spaces with 1-unconditional bases lushness, the alternative Daugavet property and numerical index~1 are equivalent. In the class of rearrangement invariant (r.i.)\ sequence spaces the only examples of spaces with these properties are ...
Kadets, Vladimir +3 more
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A new characterization of the Muckenhoupt Ap weights through an extension of the Lorentz-Shimogaki theorem [PDF]
, 2007 Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index αX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf .
Lerner, Andrei K., Pérez Moreno, Carlos
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