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Abstract  

Based on the concept of so-called (total) omnipresence of operators, several results on the generity of (translation-dilation) universal functions are proved. Mainly to have a unified approach to holomorphic and harmonic functions, in the first part operators on spaces of P-holomorphic functions are considered. The second part is devoted to holomorphic functions having lacunary power series structure and to holomorphic functions which are univalent in certain prescribed sets.

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Реэюме  

Если функция u(x) = u(x 1…, x n) имеет в точке x 0 второй асимптотический дифференциал, след матрицы квадратичной формы которого равен нулю, то u(x) наэывается асимптотически гармонической в точке x 0. В работе докаэана гармоничность суммируемых асимптотически гармонических функций.

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Summary  

The Hardy and mixed-norm spaces of harmonic functions on the real hyperbolic ball are characterized in terms of the tangential gradient.

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Abstract  

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.

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Armitage, D. H. and Goldstein, M. , The volume mean-value property of harmonic functions, Complex Variables Theory Appl. , 13 (1990), no. 3–4, 185–193. MR 91a :31004

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multiplier theorems for Jacobi series, Mem. Amer. Math. Soc. 64 (1986). MR 88c :42035 Muckenhoupt, B. and Stein, E. M. , Classical expansions and their relation to conjugate harmonic functions

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] Axler , S. , Bourdon , P. , Ramey , W. 1992 Harmonic Function Theory Graduate Texts in Mathematics 137 Springer-Verlag New York . [3] Beckenbach , E. F. , Reade , M. 1945 Mean

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420 Stević, S., Weighted integrals of harmonic functions, Studia Sci. Math. Hungar. 39 (2002), 87-96. CMP 1 909 149 Weighted integrals of harmonic functions

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