Multipliers on bi-parameter Haar system Hardy spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Multipliers on bi-parameter Haar system Hardy spaces
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Annalen
ISSN
0025-5831
e-ISSN
1432-1807
Volume of the periodical
390
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
84
Pages from-to
5669-5752
UT code for WoS article
001234596800001
EID of the result in the Scopus database
2-s2.0-85194485429