Previous |  Up |  Next

Article

Title: Optimal Sobolev embeddings (English)
Author: Pick, Luboš
Language: English
Journal: Nonlinear Analysis, Function Spaces and Applications
Volume: Vol. 6
Issue: 1998
Year:
Pages: 156-199
.
Category: math
.
MSC: 26D10
MSC: 46E30
MSC: 46E35
MSC: 47G10
idZBL: Zbl 0964.46012
idMR: MR1777715
.
Date available: 2009-10-08T09:47:40Z
Last updated: 2012-08-03
Stable URL: http://hdl.handle.net/10338.dmlcz/702465
.
Reference: [Ad] Adams D.R. : A sharp inequality of J. Moser for higher order derivatives.Annals of Math. 128 (1988), 385–398. Zbl 0672.31008, MR 0960950
Reference: [Av] Avantaggiati A. : On compact imbedding theorems in weighted Sobolev spaces.Czechoslovak Math. J. 29 (104) (1979), 635–648. MR 0548224
Reference: [BR] Bennett C., Rudnick K. : On Lorentz-Zygmund spaces.Dissert. Math. 175 (1980), 1–72. Zbl 0456.46028, MR 0576995
Reference: [BS] Bennett C., Sharpley R. : Interpolation of Operators.Academic Press, Boston 1988. Zbl 0647.46057, MR 0928802
Reference: [B] Boyd D. W. : Indices of function spaces and their relationship to interpolation.Canad. J. Math. 21 (1969), 1245–1254. Zbl 0184.34802, MR 0412788
Reference: [BW] Brézis H., Wainger S. : A note on limiting cases of Sobolev embeddings and convolution inequalities.Comm. Partial Diff. Eq. 5 (1980), 773–789. Zbl 0437.35071, MR 0579997
Reference: [Ca] Calderón A. P. : Spaces between $L^1$ and $L^\infty $ and the theorem of Marcinkiewicz.Studia Math. 26 (1966), 273–299. MR 0203444
Reference: [CPSS] Carro M. J., Pick L., Soria J., Stepanov V. D. : On embeddings between classical Lorentz spaces.Centre de Recerca Barcelona, preprint no. 385 (1998), 1–36. MR 1841071
Reference: [Ci] Cianchi A. : A sharp embedding theorem for Orlicz-Sobolev spaces.Indiana Univ. Math. J. 45 (1996), 39–65. Zbl 0860.46022, MR 1406683
Reference: [CPi] Cianchi A., Pick L. : Sobolev embeddings into.BMO, VMO, and $L_\infty $. Ark. Mat. 36 (1998), 317–340. Zbl 1035.46502, MR 1650446
Reference: [CPu] Cwikel M., Pustylnik E. : Sobolev type embeddings in the limiting case.To appear in J. Fourier Anal. Appl. Zbl 0930.46027, MR 1658620
Reference: [EGO] Edmunds D. E., Gurka P., Opic B. : Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces.Indiana Univ. Math. J. 44 (1995), 19–43. Zbl 0826.47021, MR 1336431
Reference: [EKP] Edmunds D. E., Kerman R. A., Pick L. : Optimal Sobolev embeddings involving rearrangement-invariant quasinorms.To appear. MR 1740655
Reference: [EOP] Evans W. D., Opic B., Pick L. : Interpolation of operators on scales of generalized Lorentz-Zygmund spaces.Math. Nachr. 182 (1996), 127–181. Zbl 0865.46016, MR 1419893
Reference: [F] Fiorenza A. : A summability condition on the gradient ensuring $BMO$.To appear in Rev. Mat. Univ. Complut. Madrid. Zbl 0926.46028
Reference: [GHS] dman M. L. Gol,’ Heinig H. P., Stepanov V. D. : On the principle of duality in Lorentz spaces.Canad. J. Math. 48 (1996), 959–979. MR 1414066
Reference: [H] Hansson K. : Imbedding theorems of Sobolev type in potential theory.Math. Scand. 45 (1979), 77–102. Zbl 0437.31009, MR 0567435
Reference: [HMT] Hempel J. A., Morris G. R., Trudinger N. S. : On the sharpness of a limiting case of the Sobolev imbedding theorem.Bull. Australian Math. Soc. 3 (1970), 369–373. Zbl 0205.12801, MR 0280998
Reference: [JN] John F., Nirenberg L. : On functions of bounded mean oscillation., Comm. Pure Appl. Math. 14 (1961), 415–426. Zbl 0102.04302, MR 0131498
Reference: [Ka] Kabaila V. P. : On embeddings of the space $L_p(\mu )$ into $L_r(\nu )$.(Russian). Lit. Mat. Sb. 21 (1981), 143–148. MR 0641511
Reference: [Ke1] Kerman R. A. : Function spaces continuously paired by operators of convolution-type.Canad. Math. Bull. 22 (1979), 499–507. Zbl 0428.46024, MR 0563765
Reference: [Ke2] Kerman R. A. : An integral extrapolation theorem with applications.Studia Math. 76 (1983), 183–195. Zbl 0479.46015, MR 0729102
Reference: [M] Maz’ya V. G. : Sobolev Spaces.Springer-Verlag, Berlin 1985. MR 0817985
Reference: [O] Neil R. O,’ : Convolution operators and $L_{(p,q)}$ spaces.Duke Math. J. 30 (1963), 129–142. MR 0146673
Reference: [OK] Opic B., Kufner A. : Hardy-type inequalities.Pitman Research Notes in Mathematics, Longman Sci & Tech. Harlow 1990. Zbl 0698.26007, MR 1069756
Reference: [OP] Opic B., Pick L. : On generalized Lorentz-Zygmund spaces.To appear. Zbl 0956.46020, MR 1698383
Reference: [Pe] Peetre J. : Espaces d’interpolation et théorème de Soboleff.Ann. Inst. Fourier 16 (1966), 279–317. Zbl 0151.17903, MR 0221282
Reference: [Po] Pokhozhaev S. I. : On eigenfunctions of the equation $\Delta u+\lambda f(u)=0$.(Russian). Dokl. Akad. Nauk SSSR 165 (1965), 36–39. MR 0192184
Reference: [Pu] Preprint E. Pustylnik : Optimal interpolation in spaces of Lorentz-Zygmund type., 1998, ,. MR 1749309
Reference: [Sa] Sawyer E. T. : Boundedness of classical operators on classical Lorentz spaces.Studia Math. 96 (1990), 145–158. Zbl 0705.42014, MR 1052631
Reference: [Sh] Sharpley R. : Counterexamples for classical operators in Lorentz-Zygmund spaces.Studia Math. 68 (1980), 141–158. MR 0599143
Reference: [Sob] Sobolev S. L. : Applications of Functional Analysis in Mathematical Physics.Transl. of Mathem. Monographs, American Math. Soc., Providence, RI 7 (1963). Zbl 0123.09003, MR 0165337
Reference: [Sor] Soria J. : Lorentz spaces of weak-type.Quart. J. Math. Oxford 49 (1998), 93–103. Zbl 0943.42010, MR 1617343
Reference: [St] Stepanov V. D. : The weighted Hardy inequality for nonincreasing functions.Trans. Amer. Math. Soc. 338 (1993), 173–186. MR 1097171
Reference: [Str] Strichartz R. S. : A note on Trudinger’s extension of Sobolev’s inequality.Indiana Univ. Math. J. 21 (1972), 841–842. MR 0293389
Reference: [Ta] Talenti G. : Inequalities in rearrangement-invariant function spaces.In: Nonlinear Analysis, Function Spaces and Applications, Vol. 5. M. Krbec, A. Kufner, B. Opic and J. Rákosník (eds.), Prometheus Publishing House, Prague 1995, 177–230. MR 1322313
Reference: [Tr] Trudinger N. S. : On imbeddings into Orlicz spaces and some applications.J. Math. Mech. 17 (1967), 473–483. Zbl 0163.36402, MR 0216286
Reference: [W] Wainger S. : Special trigonometric series in $k$-dimension.Mem. Amer. Math. Soc. 59 (1965), 1–102. MR 0182838
Reference: [Y] operators V. I. Yudovich : Some estimates connected with integral, 1961, with solutions of elliptic equations.Soviet Math. Doklady 2 (,) 749, 746–,.
Reference: [Z] Ziemer W. P. : Weakly differentiable functions.Graduate texts in Math. 120, Springer, New York 1989. Zbl 0692.46022, MR 1014685
Reference: [Zy] Zygmund A. : Trigonometric Series.Cambridge University Press, Cambridge 1957.
.

Files

Files Size Format View
NAFSA_098-1998-1_7.pdf 462.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo