An Extremal Problem for Integrals on a Measure Space with Abstract Parameters

Gershon Kresin

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

2 اقتباسات (Scopus)

ملخص

An extremal problem for integrals on a measure space with parameters y,y0∈Y is considered, where Y is a set of points. A class of integrands for which the integral attains its supremum over y∈ Y at a fixed point y0 is described. The integrands of such kind in Rn and on the unit sphere Sn - 1 in Rn with vector parameters are pointed out. As applications, we give a new simple proof of the sharp real-part estimate for analytic functions from the Hardy spaces in the upper half-plane as well as a solution of the extremal problem for some integrals on Sn - 1 with vector parameters. As consequence, we find the sharp constant in a pointwise estimate for solutions of the Lamé system in the upper half-space of Rn with boundary data from Lp for the case p= (n+ 2 m) / (2 m) , where m is a positive integer.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)1477-1490
عدد الصفحات14
دوريةComplex Analysis and Operator Theory
مستوى الصوت11
رقم الإصدار7
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 أكتوبر 2017

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