Inequalities in rearrangement invariant function spaces

Nonlinear Analysis, Function Spaces and Applications, GDML_Books, (1994), p. 177-230 / Harvested from

EUDML-ID : urn:eudml:doc:220022
Mots clés:

@article{702457,
     title = {Inequalities in rearrangement invariant function spaces},
     booktitle = {Nonlinear Analysis, Function Spaces and Applications},
     series = {GDML\_Books},
     publisher = {Prometheus Publishing House},
     address = {Praha},
     year = {1994},
     pages = {177-230},
     mrnumber = {MR1322313},
     zbl = {0872.46020},
     url = {http://dml.mathdoc.fr/item/702457}
}

Talenti, Giorgio. Inequalities in rearrangement invariant function spaces, dans Nonlinear Analysis, Function Spaces and Applications, GDML_Books,  (1994), pp. 177-230. http://gdmltest.u-ga.fr/item/702457/

Bibliographie

Baernstein, A. A unified approach to symmetrization, To appear in a forthcoming volume of Sympos. Math. | Zbl 0830.35005

McLeod, J.B. Rearrangements and extreme values of Dirichlet norms, Unpublished.

Talenti, G. On functions whose gradients have a prescribed rearrangement, Inequalities and Applications, World Scientific Publishing Co., to appear. | MR 1299585 | Zbl 0886.49009

Bliss, G.A. An integral inequality, J. London Math. Soc. 5 (1930), 40–46. (1930) | MR 1574997

Riesz, F. Sur une inégalité intégrale, J. London Math. Soc. 5 (1930), 162–168. (1930) | MR 1574064

Sobolev, S.L. On a theorem in functional analysis, Mat. Sb. 4 (1938), 471–497. (1938)

Lorentz, G.G. Some new functional spaces, Ann. of Math. 51 (1950), 37–55. (1950) | MR 0033449 | Zbl 0035.35602

Lorentz, G.G. On the theory of spaces $Λ$ , Pacific J. Math. 1 (1951), 411–429. (1951) | MR 0044740 | Zbl 0043.11302

Pólya, G.; Szegö, G. Isoperimetric inequalities in mathematical physics, Princeton Univ. Press, 1951. (1951) | MR 0043486

Federer, H.; Fleming, W.H. Normal and integral currents, Ann. of Math. 72 (1960), 458–520. (1960) | MR 0123260 | Zbl 0187.31301

O, R. ’Nei Convolution operators and $L (p, q)$ spaces, Duke Math. J. 30 (1963), 129–142. (1963) | MR 0146673

O, R. ’Nei; Weiss, G. The Hilbert transform and rearrangements of functions, Studia Math. 23 (1963), 189–198. (1963) | MR 0160084

Sobolev, S.L. Applications of functional analysis in mathematical physics, Translations of Mathematical Monographs, Vol. 7, Amer. Math. Soc., 1963. (1963) | MR 0165337 | Zbl 0123.09003

Hardy, G.H.; Littlewood, J.E.; Pólya, G. Inequalities, Cambridge Univ. Press, 1964. (1964)

Luxemburg, W.A.J.; Zaanen, A.C. Notes on Banach function spaces, Indag. Math. 25, 26, 27 (1965, 1966, 1967). (1965, 1966, 1967)

Hunt, R. On $L (p, q)$ spaces, Enseign. Math. 12 (1966), 249–276. (1966) | MR 0223874 | Zbl 0181.40301

Morrey, Ch.B. Multiple integrals in the calculus of variations, Grundlehren der Mathematischen Wissenschaften, Vol. 130, Springer-Verlag, New York, 1966. (1966) | MR 0202511 | Zbl 0142.38701

Herz, C. The Hardy-Littlewood maximal theorem, Symposium on harmonic analysis, Univ. of Warwick, 1968. (1968)

Federer, H. Geometric measure theory, Grundlehren der Mathematischen Wissenschaften, Vol. 153, Springer-Verlag, New York, 1969. (1969) | MR 0257325 | Zbl 0176.00801

Moser, J. A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077–1092. (1971) | MR 0301504

Stein, E.M.; Weiss, G. Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton Univ. Press, Princeton, N. J., 1971. (1971) | MR 0304972 | Zbl 0232.42007

Sperner, E. Zur Symmetrisierung für Funktionen auf Sphären, Math. Z. 134 (1973), 317–327. (1973) | MR 0340558

Spiegel, W. Über die Symmetrisierung stetiger Funktionen im Euklidischen Raum, Archiv. Math. (Basel) 24 (1973), 545–551. (1973) | MR 0412365 | Zbl 0274.52011

Brascamp, H.J.; Lieb, E.H.; Luttinger, J.M. A general rearrangement inequality for multiple integrals, J. Funct. Anal. 17 (1974), 227–237. (1974) | MR 0346109 | Zbl 0286.26005

Garsia, A.M.; Rodemich, E. Monotonicity of certain functional under rearrangements, Ann. Inst. Fourier (Grenoble) 24 (1974), 67–116. (1974) | MR 0414802

Sperner, E. Symmetrisierung für Funktionen mehrerer reeller Variablen, Manuscripta Math. 11 (1974), 159–170. (1974) | MR 0328000 | Zbl 0268.26011

Adams, R.A. Sobolev spaces, Academic Press, 1975. (1975) | MR 0450957 | Zbl 0314.46030

Aubin, T. Problèmes isopérimetriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 573–598. (1976) | MR 0448404 | Zbl 0371.46011

Hilden, K. Symmetrization of functions in Sobolev spaces and the isoperimetric inequality, Manuscripta Math. 18 (1976), 215–235. (1976) | MR 0409773 | Zbl 0365.46031

Talenti, G. Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353–372. (1976) | MR 0463908 | Zbl 0353.46018

Talenti, G. Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa 3 (1976), 697–718. (1976) | MR 0601601 | Zbl 0341.35031

Alvino, A. Sulla disuguaglianza di Sobolev in spazi di Lorentz, Boll. Uni. Mat. Ital. 5 (1977), no. 14A, 148–156. (1977) | MR 0438106

Ossermann, R. The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182–1238. (1978) | MR 0500557

Chiti, G. Rearrangements of functions and convergence in Orlicz spaces, Appl. Anal. 9 (1979), 23–27. (1979) | MR 0536688 | Zbl 0424.46023

Levine, H.A. An estimate for the best constant in a Sobolev inequality involving three integral norms, Ann. Mat. Pura Appl. 124 (1980), 181–197. (1980) | MR 0591555 | Zbl 0442.46028

Aronsson, G.; Talenti, G. Estimating the integral of a function in terms of a distribution function of its gradient, Boll. Uni. Mat. Ital. 5 (1981), no. 18B, 885–894. (1981) | MR 0641744 | Zbl 0476.49030

Lieb, E. Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. 118 (1983), 349–374. (1983) | MR 0717827 | Zbl 0527.42011

Ehrhard, A. Inégalités isopérimetriques et intégrales de Dirichlet gaussiennes, Ann. Sci. École Norm. Sup. 17 (1984), 317–332. (1984) | MR 0760680 | Zbl 0546.49020

Giarrusso, E.; Nunziante, D. Symmetrization in a class of first-order Hamilton-Jacobi equations, Nonlinear Anal. 8 (1984), 289–299. (1984) | MR 0739660 | Zbl 0543.35014

Kawohl, B. Rearrangements and convexity of level sets in PDE, Lecture Notes in Math., Vol. 1150, Springer-Verlag, Berlin – New York, 1985. (1985) | MR 0810619 | Zbl 0593.35002

Laurence, P.; Stredulinsky, E. A new approach to queer differential equations, Comm. Pure Appl. Math. 38 (1985), 333–355. (1985) | MR 0784478 | Zbl 0818.35145

Maz, V.G. ’j Sobolev spaces, Springer-Verlag, Berlin – New York, 1985. (1985) | MR 0817985

Crowe, J.A.; Zweibel, J.A. Rearrangements of functions, J. Funct. Anal. 66 (1986), 432–438. (1986) | MR 0839110 | Zbl 0612.46027

Brothers, J.; Ziemer, W. Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988), 153–179. (1988) | MR 0929981 | Zbl 0633.46030

Burago, Yu.D.; Zalgaller, V.A. Geometric inequalities, Grundlehren der Mathematischen Wissenschaften, Vol. 285, Springer-Verlag, Berlin – New York, 1988. (1988) | MR 0936419 | Zbl 0633.53002

Posteraro, M.R. Un’osservazione sul riordinamento del gradiente di una funzione, Rend. Acad. Sci. Fis. Mat. Napoli 4 (1988), no. 55, 10 pp. (1988)

Alvino, A.; Lions, P.L.; Trombetti, G. On optimization problems with prescribed rearrangements, Nonlinear Anal. 13 (1989), 185–220. (1989) | MR 0979040 | Zbl 0678.49003

Aronsson, G. An integral inequality and plastic torsion, Arch. Rational Mech. Anal. 7 (1989), 23–39. (1989) | MR 0540220

Burton, G.R. Variational problems on classes of rearrangements and multiple configurations for steady vortices, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), 295–319. (1989) | MR 0998605 | Zbl 0677.49005

Ziemer, W.P. Weakly differentiable functions, Graduate Texts in Math., Vol. 120, Springer-Verlag, New York – Berline – Heidelberg – London – Paris – Tokyo – Hong Kong, 1989. (1989) | MR 1014685 | Zbl 0692.46022

Eydeland, A.; Spruck, J.; Turkington, B. Multiconstrained variational problems of nonlinear eigenvalue type: new formulation and algorithms, Math. Comp. 55 (1990), 509–535. (1990) | MR 1035931

Ferone, V.; Posteraro, M.R. Maximization on classes of functions with fixed rearrangement, Differential Integral Equations 4 (1991), 707–718. (1991) | MR 1108055 | Zbl 0734.49002

Talenti, G. Rearrangements and partial differential equations, Inequalities (Birmingham, 1987), Lecture Notes in Pure and Appl. Math., Vol. 129, W.N. Everitt (ed.), Dekker, New York, 1991, pp. 211–230. (1991) | MR 1112579

Talenti, G. An inequality between $u^{*}$ and $| grad {u |}^{*}$ , General Inequalities, 6 (Oberwolfach, 1990), Internat. Ser. Numer. Math., Vol. 103, W. Walter (ed.), Birkhäuser, Basel, 1992, pp. 175–182. (1992) | MR 1213004 | Zbl 0783.26015

Mitrinović, D.S.; Pecarić, J.E.; Fink, A.M. Classical and new inequalities in analysis, Kluwer Academic Publishers, 1993. (1993) | MR 1220224

Pelliccia, E.; Talenti, G. A proof of a logarithmic Sobolev inequality, Calculus of Variations 1 (1993), 237–242. (1993) | MR 1261545 | Zbl 0796.49013

Talenti, G. The standard isoperimetric theorem, Handbook of Convex Geometry, P.M. Gruber & J.M. Wills (eds.), Elsevier, 1993, pp. 75–123. (1993) | MR 1242977 | Zbl 0799.51015