Clemens: Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities

Clemens, Werner:
Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities
Bollettino dell'Unione Matematica Italiana Serie 8 8-B (2005), fasc. n.3, p. 737-764, Unione Matematica Italiana (English)
pdf (716 Kb), djvu (458 Kb). | MR2182427 | Zbl 1115.26016

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Si studiano medie di funzioni con valori sulla frontiera di un insieme convesso bidimensionale. Come applicazione si prova che disuguaglianze integrali inverse implicano esattamente le stesse disuguaglianze per il riordinamento monotono. Si ottengono quindi versioni ottimali del classico lemma di Gehring, del teorema di Gurov-Reshetnyak e del teorema di Muckenhoupt.

Referenze Bibliografiche

[ApSb90] L. D'APUZZO - C. SBORDONE , Reverse Hölder Inequalities - A sharp Result, Rend. di Matematica, (Ser. 7), 10 (1990), 357-366. | MR 1076164 | Zbl 0711.42027

[BeSh88] C. BENNETT - R. Sharpley , Interpolation of Operators, Academic Press 1988, Pure and Applied Mathematics, 129. | MR 928802 | Zbl 0647.46057

[Boj85] B. BOJARSKI , Remarks on the stability of reverse Hölder inequalities and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A.I. Math., 10 (1985), 89- 94. | MR 802470 | Zbl 0582.30016

[BoIw83] B. BOJARSKI - T. IWANIEC , Analytical foundation of the theory of quasiconformal mappings in $\mathbb{R}^n$, Ann. Acad. Sci. Fenn. Ser. A. I. Math., 8 (1983), 257-324. | MR 731786 | Zbl 0548.30016

[Fio96] A. FIORENZA , Regularity Results for Minimizers of Certain One-Dimensional Lagrange Problems of Calculus of Variations, Bollettino U.M.I., (7) 10B (1996), 943-962, | MR 1430161 | Zbl 0909.49025

[FrMo85] M. FRANCIOSI - G. MOSCARIELLO , Higher integrability results, Manuscripta Math., 52 (1985), 151-170. | MR 790797 | Zbl 0576.42022

[GaRu85] C. GARCIA-CUERVA - J. L. RUBIO DE FRANCIA , Weighted norm inequalities and related topics, North-Holland Math. Studies, 116 (1985). | MR 807149 | Zbl 0578.46046

[Geh73] F.W. GEHRING , The $L^p$-integrability of the partial derivates of a quasiconformal mapping, Acta Math., 130 (1973), 265-277. | MR 402038 | Zbl 0258.30021

[Gia83] M. GIAQUINTA , Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Study, 105, Princeton Univ. Press (1983). | MR 717034 | Zbl 0516.49003

[Gia93] M. GIAQUINTA , Introduction to regularity theory for nonlinear elliptic systems Birkhäuser Verlag, Basel, Boston, Berlin 1993. | MR 1239172 | Zbl 0786.35001

[GuRe76] L. G. GUROV - YU. K. RESETNYAK , A certain analogue of the concept of a function with bounded mean oscillation Sibirsk., Math. Zh., 17, 3 (1976), 540- 546. | MR 427565 | Zbl 0341.26006

[Iwa82] T. IWANIEC , On $L^p$-integrability in PDE's and quasiregular mappings for large exponents, Ann. Acad. Sci. Fenn. Ser. A. I., 7 (1982), 301-322. | MR 686647 | Zbl 0505.30011

[Iwa98] T. IWANIEC , The Gehring Lemma, Proc. of the int. Symp., Ann Arbor, MI, USA (1998), 181-204. | MR 1488451 | Zbl 0888.30017

[IwMa01] T. IWANIEC - G. MARTIN , Geometric function theory and non-linear analysis, Oxford Math. Mono., Oxford Univ. Press, Oxford, 2001. | MR 1859913 | Zbl 1045.30011

[Kle85] I. KLEMES , A mean oscillation inequality, Proc. Am. Math. Soc., 93, Nr. 3 (1985), 497-500. | MR 774010 | Zbl 0572.46025

[Kin94] J. Kinnunen , Sharp results on reverse Hölder inequalities, Ann. Acad. Sci. Fenn., Ser. A, 1. Mathematica, Dissert., 95 (1994), 4-34. | MR 1283432 | Zbl 0816.26008

[Kol89] V.I. KOLYADA , Rearrangements of functions and imbedding theorems, Russ. Math. Surv., 44, No. 5 (1989), 73-117. | MR 1040269 | Zbl 0715.41050

[Kor92a] A. A. KORENOVSKIJ , The exact continuation of a reverse Hölder inequality and Muckenhoupt's conditions, Math. notes, 52, No. 6 (1992), 1192-1201. | MR 1208001 | Zbl 0807.42015

[Kor92b] A. A. KORENOVSKIJ , On the connection between mean value oscillation and exact integrability classes of functions, Math. USSR Sbornik, 71, No. 2 (1992), 561-567; transl. from Mat. Sb., 181, No. 12 (1990), 1721-1727. | MR 1099524 | Zbl 0776.30025

[Muc72] B. MUCKENHOUPT , Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 165 (1972), 207-226. | MR 293384 | Zbl 0236.26016

[Nan90] L. NANIA , On some reverse integral inequalities, J. Austral. Math. Soc. (Ser. A) 49 (1990), 319-326. | MR 1061052 | Zbl 0715.26010

[Sag94] H. SAGAN , Space-filling curves, Springer Verlag, New York, 1994. | MR 1299533 | Zbl 0806.01019

[Sbo86] C. SBORDONE , On some integral inequalities and their applications to the calculus of variations, Boll. Un. Mat. Ital., Ana. Func. Appl., 5-10(6,1) (1986), 73-94. | MR 897186 | Zbl 0678.49008

[Ste93] E. M. STEIN , Harmonic analysis: Real-variable methods, orthogonality and oscillatory integrals. Princeton Math. Series, 43, Princeton, New Jersey 1993. | MR 1232192 | Zbl 0821.42001

[Wik90] I. WIK , Reverse Hölder inequalities with constant close to 1, Ric. Mat., 39, No. 1 (1990), 151-157. | MR 1101311 | Zbl 0746.30022

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Referenze Bibliografiche