### Regularity of p-harmonic functions on the plane.

Tadeusz Iwaniec, Juan J. Manfredi (1989)

Revista Matemática Iberoamericana

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Tadeusz Iwaniec, Juan J. Manfredi (1989)

Revista Matemática Iberoamericana

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Feliks Przytycki, Mariusz Urbański, Anna Zdunik (1990)

Studia Mathematica

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R. Banuelos, C. N. Moore (1991)

Annales de l'institut Fourier

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We prove good-$\lambda $ inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of ${\mathbf{R}}_{+}^{2}$.

John L. Lewis, Andrew Vogel (1991)

Revista Matemática Iberoamericana

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M. Essen, D. F. Shea, C. S. Stanton (1985)

Annales de l'institut Fourier

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We give a necessary and sufficient condition for an analytic function in ${H}^{1}$ to have real part in class $L$ $logL$. This condition contains the classical one of Zygmund; other variants are also given.

Stephen J. Gardiner (1992)

Compositio Mathematica

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Mateljević, M., Vuorinen, M. (2010)

Journal of Inequalities and Applications [electronic only]

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Francesco Amoroso, Maurice Mignotte (1996)

Annales de l'institut Fourier

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Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.