Geodesic
Dorronsoro's theorem and a slight generalization
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 126-135 
D. M. Stolyarov. Dorronsoro's theorem and a slight generalization. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 126-135. http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a10/
@article{ZNSL_2015_434_a10,
     author = {D. M. Stolyarov},
     title = {Dorronsoro's theorem and a~slight generalization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--135},
     year = {2015},
     volume = {434},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a10/}
}
TY  - JOUR
AU  - D. M. Stolyarov
TI  - Dorronsoro's theorem and a slight generalization
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 126
EP  - 135
VL  - 434
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a10/
LA  - ru
ID  - ZNSL_2015_434_a10
ER  - 
%0 Journal Article
%A D. M. Stolyarov
%T Dorronsoro's theorem and a slight generalization
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 126-135
%V 434
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a10/
%G ru
%F ZNSL_2015_434_a10

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

We give a simple proof of a theorem by Dorronsoro and use similar ideas to establish the equivalence of certain embeddings results for vector fields.

[1] V. I. Kolyada, “O vlozhenii prostranstv Soboleva”, Mat. Zam., 54:3 (1993), 48–71 | MR | Zbl

[2] V. G. Mazya, T. O. Shaposhnikova, “Teoriya multiplikatorov v prostranstvakh differentsiruemykh funktsii”, UMN, 38:3(231) (1983), 23–86 | MR | Zbl

[3] D. Adams, “A note on Riesz potentials”, Duke Math. J., 42 (1975), 765–778 | DOI | MR | Zbl

[4] J. R. Dorronsoro, “Differentiability properties of functions with bounded variation”, Indiana Univ. Math. J., 38:4 (1989), 1027–1045 | DOI | MR | Zbl

[5] W. G. Faris, “Weak Lebesgue spaces and quantum mechanical binding”, Duke Math. J., 43:2 (1976), 365–373 | DOI | MR | Zbl

[6] C. Fefferman, N. M. Riviere, Y. Sagher, “Interpolation between $H^p$ spaces: the real method”, Trans. Amer. Math. Soc., 191 (1974), 71–81 | MR

[7] L. Grafakos, Classical Fourier analysis, Springer, 2008 | MR | Zbl

[8] W. Gustin, “Boxing inequalities”, J. Math. Mech., 9 (1960), 229–239 | MR | Zbl

[9] Ky Fan, “Minimax theorems”, Proc. N. A. S., 39:1 (1953), 42–47 | DOI | MR | Zbl

[10] J. van Schaftingen, “Limiting Sobolev inequalities for vector fields and cancelling linear differential operators”, J. EMS, 15:3 (2013), 877–921 | MR | Zbl

[11] J. van Schaftingen, “Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations”, J. fixed point th. appl., 15:2 (2014), 273–297 | DOI | MR | Zbl

[12] E. M. Stein, Harmonic analysis, real-variable methods, orthogonality and oscillatory integrals, Princeton University press, 1993 | MR | Zbl

[13] R. Strichartz, “$H^p$ Sobolev spaces”, Colloq. Math., 60/61 (1990), 129–139 | MR | Zbl