Geodesic
On an equivalent norm on $\mathrm{BMO}$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 37-54 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We extand the inequality proved by S. V. Bochkarev to a larger class of convolution operators, assuming that the Fourier transforms of the kernels of these operators satisfy certain conditions in the spirit of the Hörmander–Mikhlin multiplier theorem. Therefore, we give a new characterization of $\mathrm{BMO}$. 
@article{ZNSL_2017_456_a3,
     author = {I. Vasilyev and A. Tselishchev},
     title = {On an equivalent norm on~$\mathrm{BMO}$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--54},
     year = {2017},
     volume = {456},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a3/}
}
TY  - JOUR
AU  - I. Vasilyev
AU  - A. Tselishchev
TI  - On an equivalent norm on $\mathrm{BMO}$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 37
EP  - 54
VL  - 456
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a3/
LA  - ru
ID  - ZNSL_2017_456_a3
ER  - 
%0 Journal Article
%A I. Vasilyev
%A A. Tselishchev
%T On an equivalent norm on $\mathrm{BMO}$
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 37-54
%V 456
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a3/
%G ru
%F ZNSL_2017_456_a3
I. Vasilyev; A. Tselishchev. On an equivalent norm on $\mathrm{BMO}$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 45, Tome 456 (2017), pp. 37-54. http://geodesic.mathdoc.fr/item/ZNSL_2017_456_a3/

[1] L. Grafakos, Classical Fourier Analysis, 3 edition, Springer, 2014 | MR | Zbl

[2] L. Grafakos, Modern Fourier Analysis, 3 edition, Springer, 2014 | MR | Zbl

[3] Y. Han, D. Yang, “New characterization of $\mathrm{BMO}(\mathbb R^n)$ space”, Bol. Soc. Mat. Mexicana (3), 10 (2004), 95–103 | MR | Zbl

[4] S. V. Bochkarev, “Ryady Valle–Pussena v prostranstvakh $\mathrm{BMO}$, $L_1$, i $H^1(D)$, i multiplikativnye neravenstva”, Teoriya funktsii i differentsialnye uravneniya, Tr. MIAN, 210, Nauka, M., 1995, 41–64 | MR | Zbl

[5] S. V. Bochkarev, “Srednie Valle Pussena ryadov Fure dlya kvadratichnogo spektra i spektrov stepennoi plotnosti”, UMN, 69:1 (2014), 125–162 | DOI | MR | Zbl