Matches in SemOpenAlex for { <https://semopenalex.org/work/W3133600297> ?p ?o ?g. }
- W3133600297 endingPage "172" @default.
- W3133600297 startingPage "143" @default.
- W3133600297 abstract "The principal aim of this paper is to employ Bessel-type operators in proving the inequality $$displaystyle begin{aligned} int _0^pi dx , |f'(x)|{ }^2 geq dfrac {1}{4}int _0^pi dx , dfrac {|f(x)|{ }^2}{sin ^2 (x)}+dfrac {1}{4}int _0^pi dx , |f(x)|{ }^2,quad fin H_0^1 ((0,pi )), end{aligned} $$where both constants 1∕4 appearing in the above inequality are optimal. In addition, this inequality is strict in the sense that equality holds if and only if f ≡ 0. This inequality is derived with the help of the exactly solvable, strongly singular, Dirichlet-type Schrodinger operator associated with the differential expression $$displaystyle begin{aligned} tau _s=-dfrac {d^2}{dx^2}+dfrac {s^2-(1/4)}{sin ^2 (x)}, quad s in [0,infty ), ; x in (0,pi ). end{aligned} $$The new inequality represents a refinement of Hardy’s classical inequality $$displaystyle begin{aligned} int _0^pi dx , |f'(x)|{ }^2 geq dfrac {1}{4}int _0^pi dx , dfrac {|f(x)|{ }^2}{x^2}, quad fin H_0^1 ((0,pi )), end{aligned} $$and it also improves upon one of its well-known extensions in the form $$displaystyle begin{aligned} int _0^pi dx , |f'(x)|{ }^2 geq dfrac {1}{4}int _0^pi dx , dfrac {|f(x)|{ }^2}{d_{(0,pi )}(x)^2}, quad fin H_0^1 ((0,pi )), end{aligned} $$where d(0,π)(x) represents the distance from x ∈ (0, π) to the boundary {0, π} of (0, π)." @default.
- W3133600297 created "2021-03-15" @default.
- W3133600297 creator A5004675602 @default.
- W3133600297 creator A5053434924 @default.
- W3133600297 creator A5084751462 @default.
- W3133600297 date "2021-01-01" @default.
- W3133600297 modified "2023-10-16" @default.
- W3133600297 title "Bessel-Type Operators and a Refinement of Hardy’s Inequality" @default.
- W3133600297 cites W1562265198 @default.
- W3133600297 cites W1879044272 @default.
- W3133600297 cites W1985371609 @default.
- W3133600297 cites W1986214584 @default.
- W3133600297 cites W1990114462 @default.
- W3133600297 cites W1994115707 @default.
- W3133600297 cites W2009307604 @default.
- W3133600297 cites W2018483584 @default.
- W3133600297 cites W2023933547 @default.
- W3133600297 cites W2027691216 @default.
- W3133600297 cites W2038739505 @default.
- W3133600297 cites W2040781915 @default.
- W3133600297 cites W2043193384 @default.
- W3133600297 cites W2048978921 @default.
- W3133600297 cites W2054740229 @default.
- W3133600297 cites W2055265813 @default.
- W3133600297 cites W2064445172 @default.
- W3133600297 cites W2069000104 @default.
- W3133600297 cites W2082520075 @default.
- W3133600297 cites W2095071288 @default.
- W3133600297 cites W2112726937 @default.
- W3133600297 cites W2139338449 @default.
- W3133600297 cites W2200604288 @default.
- W3133600297 cites W2258304269 @default.
- W3133600297 cites W2508476950 @default.
- W3133600297 cites W2591890967 @default.
- W3133600297 cites W2836944305 @default.
- W3133600297 cites W2963553659 @default.
- W3133600297 cites W2964188734 @default.
- W3133600297 cites W3033383768 @default.
- W3133600297 cites W3103495657 @default.
- W3133600297 cites W3120583799 @default.
- W3133600297 cites W3124543428 @default.
- W3133600297 cites W3164619437 @default.
- W3133600297 cites W4232783260 @default.
- W3133600297 cites W4250633325 @default.
- W3133600297 cites W4292399988 @default.
- W3133600297 cites W4300950442 @default.
- W3133600297 cites W595184469 @default.
- W3133600297 doi "https://doi.org/10.1007/978-3-030-75425-9_9" @default.
- W3133600297 hasPublicationYear "2021" @default.
- W3133600297 type Work @default.
- W3133600297 sameAs 3133600297 @default.
- W3133600297 citedByCount "4" @default.
- W3133600297 countsByYear W31336002972021 @default.
- W3133600297 countsByYear W31336002972022 @default.
- W3133600297 crossrefType "book-chapter" @default.
- W3133600297 hasAuthorship W3133600297A5004675602 @default.
- W3133600297 hasAuthorship W3133600297A5053434924 @default.
- W3133600297 hasAuthorship W3133600297A5084751462 @default.
- W3133600297 hasBestOaLocation W31336002972 @default.
- W3133600297 hasConcept C10628310 @default.
- W3133600297 hasConcept C107706756 @default.
- W3133600297 hasConcept C118532472 @default.
- W3133600297 hasConcept C127313418 @default.
- W3133600297 hasConcept C134306372 @default.
- W3133600297 hasConcept C151730666 @default.
- W3133600297 hasConcept C202444582 @default.
- W3133600297 hasConcept C206399364 @default.
- W3133600297 hasConcept C21736991 @default.
- W3133600297 hasConcept C2777299769 @default.
- W3133600297 hasConcept C33923547 @default.
- W3133600297 hasConcept C45555294 @default.
- W3133600297 hasConcept C59037737 @default.
- W3133600297 hasConcept C78540521 @default.
- W3133600297 hasConcept C84135550 @default.
- W3133600297 hasConceptScore W3133600297C10628310 @default.
- W3133600297 hasConceptScore W3133600297C107706756 @default.
- W3133600297 hasConceptScore W3133600297C118532472 @default.
- W3133600297 hasConceptScore W3133600297C127313418 @default.
- W3133600297 hasConceptScore W3133600297C134306372 @default.
- W3133600297 hasConceptScore W3133600297C151730666 @default.
- W3133600297 hasConceptScore W3133600297C202444582 @default.
- W3133600297 hasConceptScore W3133600297C206399364 @default.
- W3133600297 hasConceptScore W3133600297C21736991 @default.
- W3133600297 hasConceptScore W3133600297C2777299769 @default.
- W3133600297 hasConceptScore W3133600297C33923547 @default.
- W3133600297 hasConceptScore W3133600297C45555294 @default.
- W3133600297 hasConceptScore W3133600297C59037737 @default.
- W3133600297 hasConceptScore W3133600297C78540521 @default.
- W3133600297 hasConceptScore W3133600297C84135550 @default.
- W3133600297 hasLocation W31336002971 @default.
- W3133600297 hasLocation W31336002972 @default.
- W3133600297 hasOpenAccess W3133600297 @default.
- W3133600297 hasPrimaryLocation W31336002971 @default.
- W3133600297 hasRelatedWork W2008732497 @default.
- W3133600297 hasRelatedWork W2021932688 @default.
- W3133600297 hasRelatedWork W2074891903 @default.
- W3133600297 hasRelatedWork W2147717648 @default.
- W3133600297 hasRelatedWork W2162290587 @default.