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Title: Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient (English)
Author: Wheeden, Richard L.
Language: English
Journal: Nonlinear Analysis, Function Spaces and Applications
Volume: Vol. 5
Issue: 1994
Year:
Pages: 231-265
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Category: math
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MSC: 26D15
MSC: 42B25
MSC: 46E35
idZBL: Zbl 0831.46032
idMR: MR1322314
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Date available: 2009-10-08T09:45:45Z
Last updated: 2012-08-03
Stable URL: http://hdl.handle.net/10338.dmlcz/702450
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Reference: [A] Adams, D. R.: A trace inequality for generalized potentials.Studia Math. 48 (1973), 99–105. Zbl 0237.46037, MR 0336316
Reference: [Ca] Calderón, C. P.: Differentiation through starlike sets in $\mathcal{R}^n$.Studia Math. 48 (1973), 1–13. MR 0330395
Reference: [Ch] Christ, M.: Weak type $(1,1)$ bounds for rough operators.Ann. of Math. 128 (1988), 19–42. Zbl 0695.47052, MR 0951506
Reference: [ChR] Christ, M., Francia, J. L. Rubio de: Weak type $(1,1)$ bounds for rough operators, II.Invent. Math. 93 (1988), 225–237. MR 0943929
Reference: [CKN] Caffarelli, L., Kohn, R., Nirenberg, L.: First order interpolation inequalities with weights.Compositio Math. 53 (1984), 259–275. Zbl 0563.46024, MR 0768824
Reference: [Cor] Córdoba, A.: Maximal functions, covering lemmas and Fourier multipliers.Proc. Sympos. Pure Math vol. 35, Amer. Math. Soc., 1979, p. 29–50. MR 0545237
Reference: [CW1] Chanillo, S., Wheeden, R. L.: Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions.Amer. J. Math. 107 (1985), 1191–1226. Zbl 0575.42026, MR 0805809
Reference: [CW2] Chanillo, S., Wheeden, R. L.: $L^p$ estimates for fractional integrals and Sobolev inequalities with applications to Schrödinger operators.Comm. Partial Differential Equations 10 (1985), 1077–1116. MR 0806256
Reference: [CW3] Chanillo, S., Wheeden, R. L.: Poincaré inequalities for a class of non-$A_p$ weights.Indiana Univ. Math. J. 41 (1992), 605–623. MR 1189903
Reference: [CWaW] Chanillo, S., Watson, D. K., Wheeden, R. L.: Some integral and maximal operators related to starlike sets.Studia Math. 107 (1993), 223–255. Zbl 0809.42008, MR 1247201
Reference: [CWiWo] Chang, S. Y. A., Wilson, J. M., Wolff, T. H.: Some weighted norm inequalities concerning the Schrödinger operators.Comment. Math. Helv. 60 (1985), 217–246. Zbl 0575.42025, MR 0800004
Reference: [DS] David, G., Semmes, S.: Strong $A_\infty $ weights, Sobolev inequalities and quasiconformal mappings.Analysis and Partial Differential Equations, Lecture Notes in Math. vol. 242, Springer-Verlag, 1971, p. 1–158.
Reference: [F] Federer, H.: Geometric Measure Theory.Springer-Verlag, New York, 1969. Zbl 0176.00801, MR 0257325
Reference: [FGaW] Franchi, B., Gallot, S., Wheeden, R. L.: Sobolev and isoperimetric inequalities for degenerate metrics.Math. Ann. (to appear). Zbl 0830.46027, MR 1314734
Reference: [FGuW] Franchi, B., Gutierrez, C., Wheeden, R. L.: Weighted Sobolev–Poincaré inequalities for Grushin type operators.Comm. Partial Differential Equations 19 (1994), 523–604. Zbl 0822.46032, MR 1265808
Reference: [FKS] Fabes, E. B., Kenig, C., Serapioni, R.: The local regularity of solutions of degenerate elliptic equations.Comm. Partial Differential Equations 7 (1982), 77–116. Zbl 0498.35042, MR 0643158
Reference: [FL] Franchi, B., Lanconelli, E.: An embedding theorem for Sobolev spaces related to non-smooth vector fields and Harnack inequality.Comm. Partial Differential Equations 9 (1984), 1237–1264. Zbl 0589.46023, MR 0764663
Reference: [FLW] Franchi, B., Lu, G., Wheeden, R. L.: Representation formulas and Poincaré inequalities for Hörmander vector fields.(to appear).
Reference: [FS] Franchi, B., Serapioni, R.: Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical approach.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), no. 3, 527–568. Zbl 0685.35046, MR 0963489
Reference: [GaK] Gabidzashvili, M., Kokilashvili, V.: Two weight weak type inequalities for fractional type integrals.Preprint no. 45, Mathematical Institute Czech Acad. Sci., Praha, 1989, pp. 1–11.
Reference: [GGK] Genebashvili, I., Gogatishvili, A., Kokilashvili, V.: Criteria of general weak type inequalities for integral operators with positive kernels.Proc. Georgian Acad. Sci. Math. 1 (1993), 11–34. MR 1251491
Reference: [GI] Greco, L., Iwaniec, T.: New inequalities for the Jacobian.preprint, 1993. MR 1259100
Reference: [GW] Gatto, E. A., Wheeden, R. L.: Sobolev inequalities for products of powers.Trans. Amer. Math. Soc. 314 (1989), 727–743. Zbl 0686.46020, MR 0967312
Reference: [J] Jerison, D.: The Poincaré inequality for vector fields satisfying Hörmander’s condition.Duke Math. J. 53 (1986), 503–523. Zbl 0614.35066, MR 0850547
Reference: [L] Luecking, D. H.: Embedding derivatives of Hardy spaces into Lebesgue spaces.Proc. London Math. Soc. 63 (1991), 595–619. Zbl 0774.42011, MR 1127151
Reference: [MW] Muckenhoupt, B., Wheeden, R. L.: Weighted norm inequalities for fractional integrals.Trans. Amer. Math. Soc. 192 (1974), 261–275. Zbl 0289.26010, MR 0340523
Reference: [P1] Perez, C.: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal maximal operator between weighted $L^p$–spaces with different weights.(to appear).
Reference: [P2] Perez, C.: Two weighted inequalities for potential and fractional type maximal operators.Indiana Univ. Math. J. (to appear). Zbl 0809.42007, MR 1291534
Reference: [P3] Perez, C.: A remark on weighted inequalities for general maximal operators.Proc. Amer. Math. Soc. (to appear). Zbl 0810.42008, MR 1107275
Reference: [S] Sawyer, E. T.: A characterization of a two-weight norm inequality for maximal operators.Studia Math. 75 (1982), 1–11. Zbl 0508.42023, MR 0676801
Reference: [Sh] Shirokov, N. A.: Some embedding theorems for spaces of harmonic functions.Zap. Nauchn. Sem. LOMI 56 (1976), 191–194. Zbl 0343.31003, MR 0481058
Reference: [St] Stein, E. M.: Note on the class $L\log L$.Studia Math. 31 (1969), 305–310. Zbl 0182.47803, MR 0247534
Reference: [SW1] Sawyer, E. T., Wheeden, R. L.: Carleson conditions for the Poisson integral.Indiana Univ. Math. J. 40 (1991), 639–676. Zbl 0748.42009, MR 1119192
Reference: [SW2] Sawyer, E. T., Wheeden, R. L.: Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces.Amer. J. Math. 114 (1992), 813–834. Zbl 0783.42011, MR 1175693
Reference: [SWZ] Sawyer, E. T., Wheeden, R. L., Zhao, S.: Weighted norm inequalities for operators of potential type and fractional maximal functions.(to appear). Zbl 0873.42012, MR 1437584
Reference: [U] Uchiyma, A.: Extension of the Hardy–Littlewood–Fefferman–Stein inequality.Pacific J. Math. 120 (1985), 229–255. MR 0808940
Reference: [V] Verbitsky, I.: Imbedding theorems for the spaces of analytic functions with mixed norms.preprint, Acad. Sci., Kishinev, Moldova, 1987.
Reference: [W1] Wheeden, R. L.: A characterization of some weighted norm inequalities for the fractional maximal function.Studia Math. 107 (1993), 251–272. Zbl 0809.42009, MR 1247202
Reference: [W2] Wheeden, R. L.: Norm inequalities for off-centered maximal operators.Publ. Matemàtiques 37 (1993), 429–441. Zbl 0848.42013, MR 1249242
Reference: [Wa1] Watson, D.: Vector-valued inequalities, factorization, and extrapolation for a family of rough operators.J. Funct. Anal. (to appear). Zbl 0811.47050, MR 1272132
Reference: [Wa2] Watson, D.: $A_1$ weights and weak type $(1,1)$ estimates for rough operators.(to appear).
Reference: [Wi] Wilson, J. M.: Weighted norm inequalities for the continuous square function.Trans. Amer. Math. Soc. 314 (1989), 661–692. MR 0972707
Reference: [WWi] Wheeden, R. L., Wilson, J. M.: $L^p$, $L^q$ weighted norm inequalities for Bergman spaces.(to appear). Zbl 0920.42015
Reference: [Z] Zani, S. L.: Weighted norm inequalities and boundary estimates for a class of positive operators and for fractional maximal functions on homogeneous spaces.Ph.D. thesis, Rutgers Univ., Dec., 1993.
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