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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Universidad de La Frontera. Departamento de Matemática y Estadística.
2022
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oai:scielo:S0719-064620220001001152022-05-13Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinementsGesztesy,FritzMichael,IsaacPang,Michael M. H. Birman-Hardy-Rellich inequalities 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.24 n.1 20222022-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462022000100115en10.4067/S0719-06462022000100115 |
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Gesztesy,Fritz Michael,Isaac Pang,Michael M. H. |
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Gesztesy,Fritz Michael,Isaac Pang,Michael M. H. Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| author_facet |
Gesztesy,Fritz Michael,Isaac Pang,Michael M. H. |
| author_sort |
Gesztesy,Fritz |
| title |
Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| title_short |
Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| title_full |
Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| title_fullStr |
Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| title_full_unstemmed |
Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements |
| title_sort |
optimality of constants in power-weighted birman-hardy-rellich-type inequalities with logarithmic refinements |
| description |
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. |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
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2022 |
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http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462022000100115 |
| work_keys_str_mv |
AT gesztesyfritz optimalityofconstantsinpowerweightedbirmanhardyrellichtypeinequalitieswithlogarithmicrefinements AT michaelisaac optimalityofconstantsinpowerweightedbirmanhardyrellichtypeinequalitieswithlogarithmicrefinements AT pangmichaelmh optimalityofconstantsinpowerweightedbirmanhardyrellichtypeinequalitieswithlogarithmicrefinements |
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1755998685194354688 |