Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient
- Nonlinear Analysis, Function Spaces and Applications, Publisher: Prometheus Publishing House(Praha), page 231-265
Access Full Article
topHow to cite
topWheeden, Richard L.. "Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient." Nonlinear Analysis, Function Spaces and Applications. Praha: Prometheus Publishing House, 1994. 231-265. <http://eudml.org/doc/221635>.
@inProceedings{Wheeden1994,
author = {Wheeden, Richard L.},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Nonlinear analysis; Function spaces; Proceedings; Spring school; Prague (Czech Republic)},
location = {Praha},
pages = {231-265},
publisher = {Prometheus Publishing House},
title = {Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient},
url = {http://eudml.org/doc/221635},
year = {1994},
}
TY - CLSWK
AU - Wheeden, Richard L.
TI - Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1994
CY - Praha
PB - Prometheus Publishing House
SP - 231
EP - 265
KW - Nonlinear analysis; Function spaces; Proceedings; Spring school; Prague (Czech Republic)
UR - http://eudml.org/doc/221635
ER -
References
top- Adams, D. R., A trace inequality for generalized potentials, Studia Math. 48 (1973), 99–105. (1973) Zbl0237.46037MR0336316
- Calderón, C. P., Differentiation through starlike sets in , Studia Math. 48 (1973), 1–13. (1973) MR0330395
- Christ, M., Weak type bounds for rough operators, Ann. of Math. 128 (1988), 19–42. (1988) Zbl0695.47052MR0951506
- Christ, M., Francia, J. L. Rubio de, Weak type bounds for rough operators, II, Invent. Math. 93 (1988), 225–237. (1988) MR0943929
- Caffarelli, L., Kohn, R., Nirenberg, L., First order interpolation inequalities with weights, Compositio Math. 53 (1984), 259–275. (1984) Zbl0563.46024MR0768824
- Córdoba, A., Maximal functions, covering lemmas and Fourier multipliers, Proc. Sympos. Pure Math vol. 35, Amer. Math. Soc., 1979, p. 29–50. (1979) MR0545237
- Chanillo, S., Wheeden, R. L., Weighted Poincaré and Sobolev inequalities and estimates for weighted Peano maximal functions, Amer. J. Math. 107 (1985), 1191–1226. (1985) Zbl0575.42026MR0805809
- Chanillo, S., Wheeden, R. L., estimates for fractional integrals and Sobolev inequalities with applications to Schrödinger operators, Comm. Partial Differential Equations 10 (1985), 1077–1116. (1985) MR0806256
- Chanillo, S., Wheeden, R. L., Poincaré inequalities for a class of non- weights, Indiana Univ. Math. J. 41 (1992), 605–623. (1992) MR1189903
- Chanillo, S., Watson, D. K., Wheeden, R. L., Some integral and maximal operators related to starlike sets, Studia Math. 107 (1993), 223–255. (1993) Zbl0809.42008MR1247201
- 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. (1985) Zbl0575.42025MR0800004
- David, G., Semmes, S., Strong weights, Sobolev inequalities and quasiconformal mappings, Analysis and Partial Differential Equations, Lecture Notes in Math. vol. 242, Springer-Verlag, 1971, p. 1–158. (1971)
- Federer, H., Geometric Measure Theory, Springer-Verlag, New York, 1969. (1969) Zbl0176.00801MR0257325
- Franchi, B., Gallot, S., Wheeden, R. L., Sobolev and isoperimetric inequalities for degenerate metrics, Math. Ann. (to appear). (to appear) Zbl0830.46027MR1314734
- Franchi, B., Gutierrez, C., Wheeden, R. L., Weighted Sobolev–Poincaré inequalities for Grushin type operators, Comm. Partial Differential Equations 19 (1994), 523–604. (1994) Zbl0822.46032MR1265808
- Fabes, E. B., Kenig, C., Serapioni, R., The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), 77–116. (1982) Zbl0498.35042MR0643158
- 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. (1984) Zbl0589.46023MR0764663
- Franchi, B., Lu, G., Wheeden, R. L., Representation formulas and Poincaré inequalities for Hörmander vector fields, (to appear). (to appear)
- 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. (1987) Zbl0685.35046MR0963489
- 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. (1989)
- 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. (1993) MR1251491
- Greco, L., Iwaniec, T., New inequalities for the Jacobian, preprint, 1993. (1993) MR1259100
- Gatto, E. A., Wheeden, R. L., Sobolev inequalities for products of powers, Trans. Amer. Math. Soc. 314 (1989), 727–743. (1989) Zbl0686.46020MR0967312
- Jerison, D., The Poincaré inequality for vector fields satisfying Hörmander’s condition, Duke Math. J. 53 (1986), 503–523. (1986) Zbl0614.35066MR0850547
- Luecking, D. H., Embedding derivatives of Hardy spaces into Lebesgue spaces, Proc. London Math. Soc. 63 (1991), 595–619. (1991) Zbl0774.42011MR1127151
- Muckenhoupt, B., Wheeden, R. L., Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261–275. (1974) Zbl0289.26010MR0340523
- Perez, C., On sufficient conditions for the boundedness of the Hardy-Littlewood maximal maximal operator between weighted –spaces with different weights, (to appear). (to appear)
- Perez, C., Two weighted inequalities for potential and fractional type maximal operators, Indiana Univ. Math. J. (to appear). (to appear) Zbl0809.42007MR1291534
- Perez, C., A remark on weighted inequalities for general maximal operators, Proc. Amer. Math. Soc. (to appear). (to appear) Zbl0810.42008MR1107275
- Sawyer, E. T., A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1–11. (1982) Zbl0508.42023MR0676801
- Shirokov, N. A., Some embedding theorems for spaces of harmonic functions, Zap. Nauchn. Sem. LOMI 56 (1976), 191–194. (1976) Zbl0343.31003MR0481058
- Stein, E. M., Note on the class , Studia Math. 31 (1969), 305–310. (1969) Zbl0182.47803MR0247534
- Sawyer, E. T., Wheeden, R. L., Carleson conditions for the Poisson integral, Indiana Univ. Math. J. 40 (1991), 639–676. (1991) Zbl0748.42009MR1119192
- Sawyer, E. T., Wheeden, R. L., Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813–834. (1992) Zbl0783.42011MR1175693
- Sawyer, E. T., Wheeden, R. L., Zhao, S., Weighted norm inequalities for operators of potential type and fractional maximal functions, (to appear). (to appear) Zbl0873.42012MR1437584
- Uchiyma, A., Extension of the Hardy–Littlewood–Fefferman–Stein inequality, Pacific J. Math. 120 (1985), 229–255. (1985) MR0808940
- Verbitsky, I., Imbedding theorems for the spaces of analytic functions with mixed norms, preprint, Acad. Sci., Kishinev, Moldova, 1987. (1987)
- Wheeden, R. L., A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), 251–272. (1993) Zbl0809.42009MR1247202
- Wheeden, R. L., Norm inequalities for off-centered maximal operators, Publ. Matemàtiques 37 (1993), 429–441. (1993) Zbl0848.42013MR1249242
- Watson, D., Vector-valued inequalities, factorization, and extrapolation for a family of rough operators, J. Funct. Anal. (to appear). (to appear) Zbl0811.47050MR1272132
- Watson, D., weights and weak type estimates for rough operators, (to appear). (to appear)
- Wilson, J. M., Weighted norm inequalities for the continuous square function, Trans. Amer. Math. Soc. 314 (1989), 661–692. (1989) MR0972707
- Wheeden, R. L., Wilson, J. M., , weighted norm inequalities for Bergman spaces, (to appear). (to appear) Zbl0920.42015
- 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. (Dec., 1993)
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.