Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements
ABSTRACT The principal aim of this paper is to establish the optimality (i.e., sharpness) of the constants A(m, α) and B(m, α), m ∈ ℕ, α ∈ ℝ, of the form in the power-weighted Birman-Hardy-Rellich-type integral inequalities with logarithmic refinement terms recently proved in [41], namely, Here the iterated logarithms are given by and the iterated exponentials are defined via Moreover, we prove the analogous sequence of inequalities on the exterior interval (r,∞) for f ∈ C ∞ 0 ((r,∞)), r ∈ (0, ∞), and once again prove optimality of the constants involved.
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| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2022
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462022000100115 |
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