Adjacent dyadic systems and the $L^{p}$-boundedness of shift operators in metric spaces revisited

Olli Tapiola

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Displaying similar documents to “Adjacent dyadic systems and the $L^{p}$ -boundedness of shift operators in metric spaces revisited”

On the tangency of sets in generalized metric spaces for certain functions of the class $F_{ρ}^{*}$

T. Konik (1991)

Matematički Vesnik

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Isometric embeddings of a class of separable metric spaces into Banach spaces

Sophocles K. Mercourakis, Vassiliadis G. Vassiliadis (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let $(M, d)$ be a bounded countable metric space and $c > 0$ a constant, such that $d (x, y) + d (y, z) - d (x, z) \geq c$ , for any pairwise distinct points $x, y, z$ of $M$ . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of $ℓ_{\infty}$ .

Metric unconditionality and Fourier analysis

Stefan Neuwirth (1998)

Studia Mathematica

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We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces $L_{E}^{p} ()$ and $C_{E} ()$ of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces $p_{E} ()$ , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between $L_{E}^{p} ()$ ...

About $w c s$ -covers and $w c s^{*}$ -networks on the Vietoris hyperspace $ℱ (X)$

Luong Quoc Tuyen, Ong V. Tuyen, Phan D. Tuan, Nguzen X. Truc (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study some generalized metric properties on the hyperspace $ℱ (X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. We prove that $X$ has a point-star network consisting of (countable) $w c s$ -covers if and only if so does $ℱ (X)$ . Moreover, $X$ has a sequence of $w c s$ -covers with property $(P)$ which is a point-star network if and only if so does $ℱ (X)$ , where $(P)$ is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable....

On the characterization of harmonic functions with initial data in Morrey space

Bo Li, Jinxia Li, Bolin Ma, Tianjun Shen (2024)

Czechoslovak Mathematical Journal

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Let $(X, d, μ)$ be a metric measure space satisfying the doubling condition and an $L^{2}$ -Poincaré inequality. Consider the nonnegative operator $ℒ$ generalized by a Dirichlet form on $X$ . We will show that a solution $u$ to $(- \partial_{t}^{2} + ℒ) u = 0$ on $X \times ℝ_{+}$ satisfies an $α$ -Carleson condition if and only if $u$ can be represented as the Poisson integral of the operator $ℒ$ with the trace in the generalized Morrey space $L^{2, α} (X)$ , where $α$ is a nonnegative function defined on a class of balls in $X$ . This result extends the analogous characterization...

Hardy-Rogers-type fixed point theorems for $α$ - $G F$ -contractions

Muhammad Arshad, Eskandar Ameer, Aftab Hussain (2015)

Archivum Mathematicum

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The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for $α$ - $η$ - $G F$ -contraction in a complete metric space. We extend the concept of $F$ -contraction into an $α$ - $η$ - $G F$ -contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.

Wasserstein metric and subordination

Philippe Clément, Wolfgang Desch (2008)

Studia Mathematica

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Let $(X, d_{X})$ , $(Ω, d_{Ω})$ be complete separable metric spaces. Denote by (X) the space of probability measures on X, by $W_{p}$ the p-Wasserstein metric with some p ∈ [1,∞), and by $_{p} (X)$ the space of probability measures on X with finite Wasserstein distance from any point measure. Let $f : Ω \to_{p} (X)$ , $ω \mapsto f_{ω}$ , be a Borel map such that f is a contraction from $(Ω, d_{Ω})$ into $(_{p} (X), W_{p})$ . Let ν₁,ν₂ be probability measures on Ω with $W_{p} (ν ₁, ν ₂)$ finite. On X we consider the subordinated measures $μ_{i} = \int_{Ω} f_{ω} d ν_{i} (ω)$ . Then $W_{p} (μ ₁, μ ₂) \leq W_{p} (ν ₁, ν ₂)$ . As an application we show that the solution measures $ϱ_{α} (t)$ ...

On almost everywhere differentiability of the metric projection on closed sets in $l^{p} (ℝ^{n})$ , $2 < p < \infty$

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

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Let $F$ be a closed subset of $ℝ^{n}$ and let $P (x)$ denote the metric projection (closest point mapping) of $x \in ℝ^{n}$ onto $F$ in $l^{p}$ -norm. A classical result of Asplund states that $P$ is (Fréchet) differentiable almost everywhere (a.e.) in $ℝ^{n}$ in the Euclidean case $p = 2$ . We consider the case $2 < p < \infty$ and prove that the $i$ th component $P_{i} (x)$ of $P (x)$ is differentiable a.e. if $P_{i} (x) \neq x_{i}$ and satisfies Hölder condition of order $1 / (p - 1)$ if $P_{i} (x) = x_{i}$ .

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

Isomorphic properties in spaces of compact operators

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the definition of $p$ -limited completely continuous operators, $1 \leq p < \infty$ . The question of whether a space of operators has the property that every $p$ -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using $p$ -limited completely continuous evaluation operators.

Spaces of compact operators on $C (2^{} \times [0, α])$ spaces

Elói Medina Galego (2011)

Colloquium Mathematicae

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We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces $2^{} \times [0, α]$ , the topological products of Cantor cubes $2^{}$ and intervals of ordinal numbers [0,α].

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^{X}$ can be extended to a Whitney map for $2^{X}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Multiplication operators on $L (L_{p})$ and $ℓ_{p}$ -strictly singular operators

William Johnson, Gideon Schechtman (2008)

Journal of the European Mathematical Society

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A classification of weakly compact multiplication operators on $L (L_{p}),$ 1<p< $, i s g i v e n . T h i s a n s w e r s a q u e s t i o n r a i s e d b y S a k s m a n a n d T y l l i i n 1992 . T h e c l a s s i f i c a t i o n i n v o l v e s t h e c o n c e p t o f$ p $- s t r i c t l y s i n g u l a r o p e r a t o r s, a n d w e a l s o i n v e s t i g a t e t h e s t r u c t u r e o f g e n e r a l$ p $- s t r i c t l y s i n g u l a r o p e r a t o r s o n$ Lp $. T h e m a i n r e s u l t i s t h a t i f a n o p e r a t o r$ T $o n$ Lp $,$ 1<p<2 $, i s$ p $- s t r i c t l y s i n g u l a r a n d$ T|X $i s a n i s o m o r p h i s m f o r s o m e s u b s p a c e$ X $o f$ Lp $, t h e n$ X $e m b e d s i n t o$ Lr $f o r a l l$ r<2 $, b u t$ X $n e e d n o t b e i s o m o r p h i c t o a H i l b e r t s p a c e .$ It is also shown that if $T$ is convolution by a biased coin on $L_{p}$ of the Cantor group, $1 \leq p < 2$ , and $T_{| X}$ is an isomorphism for some reflexive subspace $X$ of $L_{p}$ , then $X$ is isomorphic to a Hilbert space. The case $p = 1$ answers a question asked by Rosenthal in 1976.

Displaying similar documents to “Adjacent dyadic systems and the L p -boundedness of shift operators in metric spaces revisited”

Displaying similar documents to “Adjacent dyadic systems and the $L^{p}$ -boundedness of shift operators in metric spaces revisited”