Integral mean of Green’s potentials and their conjugate
Copyright policy )Integral mean of Green’s potentials and their conjugate
The best possible estimates for Lebesgue integral means $m_q(r,F)\; (1\le q<+\infty)$ for the pair of functions $F= g+i\:\breve{g}$, here $g$ - Green's potential, $\breve{g}$ - function conjugate to $g$, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk for logarithms $\log\; B$ of Blaschke products $B$ in terms of counting function $n(r,0,B)\; (0<r<1)$ of their zeroes.
Green's potentials, distribution of values of subharmonic functions, Потенціали Ґріна, спряжені функції, лебегові інтегральні середні, розподіл значень субгармонійних функцій, lebesgue integral means, green's potentials, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions, Lebesgue integral means, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Потенциалы Грина, сопряженная функция, интегральные средние Лебега, распределение значений субгармонических функций, QA1-939, conjugate function, Green's potentials, conjugate function, Lebesgue integral means, distribution of values of subharmonic functions, Harmonic, subharmonic, superharmonic functions in two dimensions, Mathematics
Green's potentials, distribution of values of subharmonic functions, Потенціали Ґріна, спряжені функції, лебегові інтегральні середні, розподіл значень субгармонійних функцій, lebesgue integral means, green's potentials, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions, Lebesgue integral means, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Потенциалы Грина, сопряженная функция, интегральные средние Лебега, распределение значений субгармонических функций, QA1-939, conjugate function, Green's potentials, conjugate function, Lebesgue integral means, distribution of values of subharmonic functions, Harmonic, subharmonic, superharmonic functions in two dimensions, Mathematics
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