Geodesic
Hausdorff operators of special kind in $BMO$-type spaces and H\"older--Lipschitz spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 8-21

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

We show that some $BMO$-type spaces are invariant with respect to the Hausdorff operators of special kind (weighted Hardy-Cesaro operators). Also we obtain a sufficient and necessary conditions for such operators to be bounded in spaces of functions of generalized bounded variation. Finally, we study the invariance of Hölder–Lipschitz spaces with respect to these operators.
Keywords: Hausdorff operator, Hölder–Lipschitz spaces, $VMO(\mathbb R^n)$, $bmo(\mathbb R^n)$, functions of generalized bounded variation. 
@article{IVM_2020_12_a1,
     author = {S. S. Volosivets},
     title = {Hausdorff operators of special kind in $BMO$-type spaces and {H\"older--Lipschitz} spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {8--21},
     publisher = {mathdoc},
     number = {12},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_12_a1/}
}
TY  - JOUR
AU  - S. S. Volosivets
TI  - Hausdorff operators of special kind in $BMO$-type spaces and H\"older--Lipschitz spaces
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 8
EP  - 21
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_12_a1/
LA  - ru
ID  - IVM_2020_12_a1
ER  - 
%0 Journal Article
%A S. S. Volosivets
%T Hausdorff operators of special kind in $BMO$-type spaces and H\"older--Lipschitz spaces
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 8-21
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_12_a1/
%G ru
%F IVM_2020_12_a1
S. S. Volosivets. Hausdorff operators of special kind in $BMO$-type spaces and H\"older--Lipschitz spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 8-21. http://geodesic.mathdoc.fr/item/IVM_2020_12_a1/