Multipliers on bi-parameter Haar system Hardy spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00382587" target="_blank" >RIV/68407700:21230/24:00382587 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00208-024-02887-9" target="_blank" >https://doi.org/10.1007/s00208-024-02887-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-024-02887-9" target="_blank" >10.1007/s00208-024-02887-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multipliers on bi-parameter Haar system Hardy spaces

Popis výsledku v původním jazyce

Let (h(I)) denote the standard Haar system on [0,1], indexed by I is an element of D, the set of dyadic intervals and h(I)circle times h(J )denote the tensor product (s,t) -> h(I)(s)h(J)(t), I, J is an element of D. We consider a class of two-parameter function spaces which are completions of the linear span V(delta(2))of h(I)circle times h(J), I, J is an element of D. This class contains all the spaces of the form X(Y), where X and Y are either the Lebesgue spaces L-p[0,1]or the Hardy spaces H-p[0,1],1 <= p < infinity. We say that D:X(Y) -> X(Y)is a Haar multiplier if D((I)(h)circle times(J)(h))=d(I), Jh(I)circle times h(J), where d(I),J is an element of R, and ask which more elementary operators factor through D. A decisive role is played by the Capon projection C:V(delta(2)) -> V(delta(2))given by Ch(I)circle times h(J)=h(I)circle times h(J )if|I| <= |J|, and Ch(I )circle times h(J)=0if|I|>|J|, as our main result highlights: Given any bounded Haar multiplier D:X(Y) -> X(Y), there exist lambda, mu is an element of R such that lambda C+mu(Id-C) approximately 1-projectionally factors through D, i.e., for all eta > 0, there exist bounded operators A, B so that AB is the identity operator Id, & Vert;A & Vert;<middle dot>& Vert;B & Vert;=1 and & Vert;lambda C+mu(Id-C)-ADB & Vert;<eta. Additionally, if C is unbounded on X(Y), then lambda=mu and then Id either factors through D or Id-D.

Název v anglickém jazyce

Multipliers on bi-parameter Haar system Hardy spaces

Popis výsledku anglicky

Let (h(I)) denote the standard Haar system on [0,1], indexed by I is an element of D, the set of dyadic intervals and h(I)circle times h(J )denote the tensor product (s,t) -> h(I)(s)h(J)(t), I, J is an element of D. We consider a class of two-parameter function spaces which are completions of the linear span V(delta(2))of h(I)circle times h(J), I, J is an element of D. This class contains all the spaces of the form X(Y), where X and Y are either the Lebesgue spaces L-p[0,1]or the Hardy spaces H-p[0,1],1 <= p < infinity. We say that D:X(Y) -> X(Y)is a Haar multiplier if D((I)(h)circle times(J)(h))=d(I), Jh(I)circle times h(J), where d(I),J is an element of R, and ask which more elementary operators factor through D. A decisive role is played by the Capon projection C:V(delta(2)) -> V(delta(2))given by Ch(I)circle times h(J)=h(I)circle times h(J )if|I| <= |J|, and Ch(I )circle times h(J)=0if|I|>|J|, as our main result highlights: Given any bounded Haar multiplier D:X(Y) -> X(Y), there exist lambda, mu is an element of R such that lambda C+mu(Id-C) approximately 1-projectionally factors through D, i.e., for all eta > 0, there exist bounded operators A, B so that AB is the identity operator Id, & Vert;A & Vert;<middle dot>& Vert;B & Vert;=1 and & Vert;lambda C+mu(Id-C)-ADB & Vert;<eta. Additionally, if C is unbounded on X(Y), then lambda=mu and then Id either factors through D or Id-D.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Svazek periodika

390

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

84

Strana od-do

5669-5752

Kód UT WoS článku

001234596800001

EID výsledku v databázi Scopus

2-s2.0-85194485429