# Article

Full entry | PDF   (0.4 MB)
References:
[A] Adams, D. R.: A trace inequality for generalized potentials. Studia Math. 48 (1973), 99–105. MR 0336316 | Zbl 0237.46037
[Ca] Calderón, C. P.: Differentiation through starlike sets in $\mathcal{R}^n$. Studia Math. 48 (1973), 1–13. MR 0330395
[Ch] Christ, M.: Weak type $(1,1)$ bounds for rough operators. Ann. of Math. 128 (1988), 19–42. MR 0951506 | Zbl 0695.47052
[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
[CKN] Caffarelli, L., Kohn, R., Nirenberg, L.: First order interpolation inequalities with weights. Compositio Math. 53 (1984), 259–275. MR 0768824 | Zbl 0563.46024
[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
[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. MR 0805809 | Zbl 0575.42026
[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
[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
[CWaW] Chanillo, S., Watson, D. K., Wheeden, R. L.: Some integral and maximal operators related to starlike sets. Studia Math. 107 (1993), 223–255. MR 1247201 | Zbl 0809.42008
[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. MR 0800004 | Zbl 0575.42025
[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.
[F] Federer, H.: Geometric Measure Theory. Springer-Verlag, New York, 1969. MR 0257325 | Zbl 0176.00801
[FGaW] Franchi, B., Gallot, S., Wheeden, R. L.: Sobolev and isoperimetric inequalities for degenerate metrics. Math. Ann. (to appear). MR 1314734 | Zbl 0830.46027
[FGuW] Franchi, B., Gutierrez, C., Wheeden, R. L.: Weighted Sobolev–Poincaré inequalities for Grushin type operators. Comm. Partial Differential Equations 19 (1994), 523–604. MR 1265808 | Zbl 0822.46032
[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. MR 0643158 | Zbl 0498.35042
[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. MR 0764663 | Zbl 0589.46023
[FLW] Franchi, B., Lu, G., Wheeden, R. L.: Representation formulas and Poincaré inequalities for Hörmander vector fields. (to appear).
[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. MR 0963489 | Zbl 0685.35046
[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.
[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
[GI] Greco, L., Iwaniec, T.: New inequalities for the Jacobian. preprint, 1993. MR 1259100
[GW] Gatto, E. A., Wheeden, R. L.: Sobolev inequalities for products of powers. Trans. Amer. Math. Soc. 314 (1989), 727–743. MR 0967312 | Zbl 0686.46020
[J] Jerison, D.: The Poincaré inequality for vector fields satisfying Hörmander’s condition. Duke Math. J. 53 (1986), 503–523. MR 0850547 | Zbl 0614.35066
[L] Luecking, D. H.: Embedding derivatives of Hardy spaces into Lebesgue spaces. Proc. London Math. Soc. 63 (1991), 595–619. MR 1127151 | Zbl 0774.42011
[MW] Muckenhoupt, B., Wheeden, R. L.: Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc. 192 (1974), 261–275. MR 0340523 | Zbl 0289.26010
[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).
[P2] Perez, C.: Two weighted inequalities for potential and fractional type maximal operators. Indiana Univ. Math. J. (to appear). MR 1291534 | Zbl 0809.42007
[P3] Perez, C.: A remark on weighted inequalities for general maximal operators. Proc. Amer. Math. Soc. (to appear). MR 1107275 | Zbl 0810.42008
[S] Sawyer, E. T.: A characterization of a two-weight norm inequality for maximal operators. Studia Math. 75 (1982), 1–11. MR 0676801 | Zbl 0508.42023
[Sh] Shirokov, N. A.: Some embedding theorems for spaces of harmonic functions. Zap. Nauchn. Sem. LOMI 56 (1976), 191–194. MR 0481058 | Zbl 0343.31003
[St] Stein, E. M.: Note on the class $L\log L$. Studia Math. 31 (1969), 305–310. MR 0247534 | Zbl 0182.47803
[SW1] Sawyer, E. T., Wheeden, R. L.: Carleson conditions for the Poisson integral. Indiana Univ. Math. J. 40 (1991), 639–676. MR 1119192 | Zbl 0748.42009
[SW2] Sawyer, E. T., Wheeden, R. L.: Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces. Amer. J. Math. 114 (1992), 813–834. MR 1175693 | Zbl 0783.42011
[SWZ] Sawyer, E. T., Wheeden, R. L., Zhao, S.: Weighted norm inequalities for operators of potential type and fractional maximal functions. (to appear). MR 1437584 | Zbl 0873.42012
[U] Uchiyma, A.: Extension of the Hardy–Littlewood–Fefferman–Stein inequality. Pacific J. Math. 120 (1985), 229–255. MR 0808940
[V] Verbitsky, I.: Imbedding theorems for the spaces of analytic functions with mixed norms. preprint, Acad. Sci., Kishinev, Moldova, 1987.
[W1] Wheeden, R. L.: A characterization of some weighted norm inequalities for the fractional maximal function. Studia Math. 107 (1993), 251–272. MR 1247202 | Zbl 0809.42009
[W2] Wheeden, R. L.: Norm inequalities for off-centered maximal operators. Publ. Matemàtiques 37 (1993), 429–441. MR 1249242 | Zbl 0848.42013
[Wa1] Watson, D.: Vector-valued inequalities, factorization, and extrapolation for a family of rough operators. J. Funct. Anal. (to appear). MR 1272132 | Zbl 0811.47050
[Wa2] Watson, D.: $A_1$ weights and weak type $(1,1)$ estimates for rough operators. (to appear).
[Wi] Wilson, J. M.: Weighted norm inequalities for the continuous square function. Trans. Amer. Math. Soc. 314 (1989), 661–692. MR 0972707
[WWi] Wheeden, R. L., Wilson, J. M.: $L^p$, $L^q$ weighted norm inequalities for Bergman spaces. (to appear). Zbl 0920.42015
[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.

Partner of