Geodesic
Piecewise General Monotone Functions and the Hardy--Littlewood Theorem
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 120-133

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain necessary and sufficient conditions for an integrable piecewise general monotone function to belong to an $L^p$ space with a weight of Muckenhoupt class $\mathbb A_p$ in terms of the Fourier coefficients. We also find a sufficient condition for the Hardy transform of an arbitrary integrable function to belong to the same space. 
@article{TRSPY_2022_319_a9,
     author = {M. I. Dyachenko and S. Yu. Tikhonov},
     title = {Piecewise {General} {Monotone} {Functions} and the {Hardy--Littlewood} {Theorem}},
     journal = {Informatics and Automation},
     pages = {120--133},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a9/}
}
TY  - JOUR
AU  - M. I. Dyachenko
AU  - S. Yu. Tikhonov
TI  - Piecewise General Monotone Functions and the Hardy--Littlewood Theorem
JO  - Informatics and Automation
PY  - 2022
SP  - 120
EP  - 133
VL  - 319
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a9/
LA  - ru
ID  - TRSPY_2022_319_a9
ER  - 
%0 Journal Article
%A M. I. Dyachenko
%A S. Yu. Tikhonov
%T Piecewise General Monotone Functions and the Hardy--Littlewood Theorem
%J Informatics and Automation
%D 2022
%P 120-133
%V 319
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a9/
%G ru
%F TRSPY_2022_319_a9
M. I. Dyachenko; S. Yu. Tikhonov. Piecewise General Monotone Functions and the Hardy--Littlewood Theorem. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 120-133. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a9/