Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition in variable exponent Sobolev spaces
| LEADER | caa a22 4500 | ||
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4488-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4488-x | ||
| 245 | 0 | 0 | |a Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition in variable exponent Sobolev spaces |h [Elektronische Daten] |c [Xia Li, Guo Lu, Han Tang] |
| 520 | 3 | |a In this paper, we will establish Poincaré inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincaré inequalities for vector fields satisfying Hörmander's condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincaré inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p(x)-subLaplacian. Our results are only stated and proved for vector fields satisfying Hörmander's condition, but they also hold for Grushin vector fields as well with obvious modifications. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Poincaré inequalities |2 nationallicence | |
| 690 | 7 | |a the representation formula |2 nationallicence | |
| 690 | 7 | |a fractional integrals on homogeneous spaces |2 nationallicence | |
| 690 | 7 | |a vector fields satisfying Hörmander's condition |2 nationallicence | |
| 690 | 7 | |a stratified groups |2 nationallicence | |
| 690 | 7 | |a high order non-isotropic Sobolev spaces with variable exponents |2 nationallicence | |
| 690 | 7 | |a Sobolev inequalities with variable exponents |2 nationallicence | |
| 700 | 1 | |a Li |D Xia |u School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, P. R. China |4 aut | |
| 700 | 1 | |a Lu |D Guo |u Department of Mathematics, Wayne State University, 48202, Detroit, MI, USA |4 aut | |
| 700 | 1 | |a Tang |D Han |u School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1067-1085 |x 1439-8516 |q 31:7<1067 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4488-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4488-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Li |D Xia |u School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Lu |D Guo |u Department of Mathematics, Wayne State University, 48202, Detroit, MI, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Tang |D Han |u School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/7(2015-07-01), 1067-1085 |x 1439-8516 |q 31:7<1067 |1 2015 |2 31 |o 10114 | ||