Geodesic
Gagliardo–Nirenberg inequality for maximal functions measuring smoothness
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 143-161 
E. Lokharu. Gagliardo–Nirenberg inequality for maximal functions measuring smoothness. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 143-161. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/
@article{ZNSL_2011_389_a8,
     author = {E. Lokharu},
     title = {Gagliardo{\textendash}Nirenberg inequality for maximal functions measuring smoothness},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {143--161},
     year = {2011},
     volume = {389},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/}
}
TY  - JOUR
AU  - E. Lokharu
TI  - Gagliardo–Nirenberg inequality for maximal functions measuring smoothness
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 143
EP  - 161
VL  - 389
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/
LA  - ru
ID  - ZNSL_2011_389_a8
ER  - 
%0 Journal Article
%A E. Lokharu
%T Gagliardo–Nirenberg inequality for maximal functions measuring smoothness
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 143-161
%V 389
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/
%G ru
%F ZNSL_2011_389_a8

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We prove a Gagliardo–Nirenberg type pointwise interpolation inequality for special maximal functions, measuring smoothness in multidimensional case. It turns out that the clissical inequality follows from this one and it is also possible to use naturally a BMO terms in the inequality.

[1] R. DeVore, R. Sharpley, Maximal functions measuring smoothness, Memoirs Amer. Math. Soc., 47, no. 293, 1984 | DOI | MR

[2] A. Calderon, R. Scott, “Sobolev type inequalities for $p>0$”, Studia Math., 62 (1978), 75–92 | MR | Zbl

[3] Y. Meyer, T. Rivière, “A partial regularity result for a class of stationary Yang–Mills fields”, Rev. Mat. Iberoamericana, 19 (2003), 195–219 | DOI | MR | Zbl

[4] A. Kalamajska, A. Milani, “Anisotropic Sobolev spaces and parabolic equations”, Ulmer Seminare über Funktionalanalysis und Differentialgleichungen, 2 (1997), 237–273

[5] A. Kalamajska, “Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces”, Studia Math., 108:3 (1994), 275–290 | MR | Zbl

[6] P. Strzelecki, “Gagliardo–Nirenberg inequalities with a $\mathrm{BMO}$ term”, Bull. London Math. Soc., 38 (2006), 294–300 | DOI | MR | Zbl