An Example of a Singular Integral and a Weight

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475587" target="_blank" >RIV/00216208:11320/23:10475587 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mrEYy5enaj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mrEYy5enaj</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnac062" target="_blank" >10.1093/imrn/rnac062</a>

Result language
angličtina
Original language name
An Example of a Singular Integral and a Weight
Original language description
Sharp weighted inequalities were recently proved for several classical operators in Harmonic analysis, however for the rough singular integral the sharp result remains open. The best bound so far was found by Hytonen, Roncal and Tapiola in [2]. For A(2) weight, it is quadratic, meaning parallel to T(Omega)f parallel to(L omega 2) <= C[omega](2)(2)parallel to f parallel to(L omega 2). The authors also conjectured that the best bound is linear. We provide example of A(2) weights omega(n), test functions f(n) and rough singular integrals T-Omega n (f)(x) = p.v. integral(R2) vertical bar y vertical bar(-2)Omega(n)(Y/vertical bar y vertical bar)f(x - y)dy, where Omega(n) is a function in L-infinity(S-1) with norm 1 and vanishing integral such that parallel to T(Omega n)f(n)parallel to(L omega n2) >= C[omega(n)](2)(3/2)parallel to f(n)parallel to(L omega n2) and [omega(n)](2) approximate to n, disproving the conjecture.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA21-01976S" target="_blank" >GA21-01976S: Geometric and Harmonic Analysis 2</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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