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On the boundary limits of harmonic functions with gradient in \(L^p\). (English) Zbl 0522.31009

MSC:
31B25 Boundary behavior of harmonic functions in higher dimensions
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
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References:
[1] L. CARLESON, Selected problems on exceptional sets, Van Nostrand, Princeton, 1967. · Zbl 0189.10903
[2] A.B. CRUZEIRO, Convergence au bord pour LES fonctions harmoniques dans rd de la classe de Sobolev wd1, C.R.A.S., Paris, 294 (1982), 71-74. · Zbl 0495.31003
[3] N.G. MEYERS, A theory of capacities for potentials in Lebesgue classes, Math. Scand., 26 (1970), 255-292. · Zbl 0242.31006
[4] N.G. MEYERS, Continuity properties of potentials, Duke Math. J., 42 (1975), 157-166. · Zbl 0334.31004
[5] Y. MIZUTA, On the existence of boundary values of beppo Levi functions defined in the upper half space of rn, Hiroshima Math. J., 6 (1976), 61-72. · Zbl 0329.31007
[6] Y. MIZUTA, Existence of various boundary limits of beppo Levi functions of higher order, Hiroshima Math. J., 9 (1979), 717-745. · Zbl 0475.31004
[7] A. NAGEL, W. RUDIN and J.H. SHAPIRO, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math., 116 (1982), 331-360. · Zbl 0531.31007
[8] M. OHTSUKA, Extremal length and precise functions in 3-space, Lecture Notes, Hiroshima Univ., 1973.
[9] E.M. STEIN, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970. · Zbl 0207.13501
[10] H. WALLIN, On the existence of boundary values of a class of beppo Levi functions, Trans. Amer. Math. Soc., 120 (1965), 510-525. · Zbl 0139.06301
[11] J.-M. G. WU, Lp-densities and boundary behaviors of Green potentials, Indiana Univ. Math. J., 28 (1979), 895-911. · Zbl 0449.31003
[12] W.P. ZIEMER, Extremal length as a capacity, Michigan Math. J., 17 (1970), 117-128. · Zbl 0183.39104
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