Geodesic
On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 221-228.

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

Conditions for the constants of best approximation in the metric of the spaces $L^p(B)$ to be continuous or semicontinuous as functions of the center of a ball $B$ of fixed radius in a metric space with Borel measure are studied.
Keywords: metric measure space, best approximations by constants. 
@article{MZM_2020_107_2_a4,
     author = {I. N. Katkovskaya and V. G. Krotov},
     title = {On the {Continuity} of {Best} {Approximations} by {Constants} on {Balls} in {Metric} {Measure} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {221--228},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/}
}
TY  - JOUR
AU  - I. N. Katkovskaya
AU  - V. G. Krotov
TI  - On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces
JO  - Matematičeskie zametki
PY  - 2020
SP  - 221
EP  - 228
VL  - 107
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/
LA  - ru
ID  - MZM_2020_107_2_a4
ER  - 
%0 Journal Article
%A I. N. Katkovskaya
%A V. G. Krotov
%T On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces
%J Matematičeskie zametki
%D 2020
%P 221-228
%V 107
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/
%G ru
%F MZM_2020_107_2_a4
I. N. Katkovskaya; V. G. Krotov. On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 221-228. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a4/

[1] C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math., 580, Springer-Verlag, Berlin, 1977 | DOI | MR | Zbl

[2] C. D. Aliprantis, K. C. Border, Infnite-Dimensional Analysis. A Hitchhiker's Guide, Springer-Verlag, Berlin, 1994 | MR

[3] I. Fonseca, G. Leoni, Modern Methods in the Calculus of Variations: $L^p$ Spaces, Springer, New York, 2007 | MR

[4] V. G. Krotov, A. I. Porabkovich, “Otsenki $L^p$-ostsillyatsii funktsii pri $p>0$”, Matem. zametki, 97:3 (2015), 407–420 | DOI | MR | Zbl

[5] S. A. Bondarev, V. G. Krotov, “Fine properties of functions from Hajłasz–Sobolev classes $M^p_{\alpha}$, $p>0$, I. Lebesgue points”, Izv. NAN Armenii. Matem., 51:6 (2016), 3–22 | MR | Zbl

[6] S. A. Bondarev, V. G. Krotov, “Fine properties of functions from Hajłasz–Sobolev classes $M^p_{\alpha}$, $p>0$, II. Lusin's approximation”, Izv. NAN Armenii. Matem., 52:1 (2017), 26–37 | MR | Zbl

[7] J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, Berlin, 2001 | MR | Zbl