On the Constants and Extremal Function and Sequence for Hardy Inequalities in L_p and l_p

2023/09/30 by Ivan Gadjev, Gadjev, Ivan
Mathematics · #15A42 #26D15 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Primary 26D10 #Secondary 33C45

paper · pdf · doi:10.48550/arxiv.2310.00281

openalex publication_date 2023/09/30 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28

Abstract

We study the behavior of the smallest possible constants d(a,b) and d_n in Hardy inequalities ∫_a^b((1)/(x)∫_a^xf(t)dt)^p dx≤ d(a,b) ∫_a^b [f(x)]^p dx and ∑_k=1ⁿ((1)/(k)∑_j=1^ka_j)^p≤ d_n ∑_k=1ⁿa_k^p. The exact rate of convergence of d(a,b) and d_n is established and the ``almost extremal'' function and sequence are found.

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