Matches in SemOpenAlex for { <https://semopenalex.org/work/W1985497716> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W1985497716 endingPage "412" @default.
- W1985497716 startingPage "394" @default.
- W1985497716 abstract "Let Ω be a fixed open cube in ℝn. For r∈[1, ∞) and α∈[0, ∞) we define ( M r ; α , Ω f ) ( x ) = sup Q x ∈ Q ⊂ Ω ‖ f χ Q ‖ L r ‖ χ Q ‖ L r ( log L ) α , x ∈ Ω where Q is a cube in ℝn (with sides parallel to the coordinate axes) and χQ stands for the characteristic function of the cube Q. A well-known result of Gehring [5] states that if ( M p ; 0 , Ω f ) ( x ) ⩽ c ( M 1 ; 0 , Ω f ) ( x ) , x ∈ Ω (1.1) for some p∈(1, ∞) and c∈(0, ∞), then there exist q∈(p, ∞) and C=C(p, q, n, c)∈(0, ∞) such that ( 1 | Q | ∫ Q | f ( x ) | q d x ) 1 / q ⩽ c 1 | Q | ∫ Q | f ( x ) | d x for all cubes Q⊂Ω, where ∣Q∣ denotes the n-dimensional Lebesgue measure of Q. In particular, a function f∈L1(Ω) satisfying (1.1) belongs to Lq(Ω). In [9] it was shown that Gehring's result is a particular case of a more general principle from the real method of interpolation. Roughly speaking, this principle states that if a certain reversed inequality between K-functionals holds at one point of an interpolation scale, then it holds at other nearby points of this scale. Using an extension of Holmstedt's reiteration formulae of [4] and results of [8] on weighted inequalities for monotone functions, we prove here two variants of this principle involving extrapolation spaces of an ordered pair of (quasi-) Banach spaces. As an application we prove the following Gehring-type lemmas." @default.
- W1985497716 created "2016-06-24" @default.
- W1985497716 creator A5037053721 @default.
- W1985497716 creator A5081865508 @default.
- W1985497716 date "1998-10-01" @default.
- W1985497716 modified "2023-09-23" @default.
- W1985497716 title "Real Interpolation and Two Variants of Gehring's Lemma" @default.
- W1985497716 cites W1499500817 @default.
- W1985497716 cites W2011504393 @default.
- W1985497716 cites W2028959607 @default.
- W1985497716 cites W2048777913 @default.
- W1985497716 cites W2064374691 @default.
- W1985497716 cites W593537426 @default.
- W1985497716 cites W99949108 @default.
- W1985497716 cites W2320590127 @default.
- W1985497716 doi "https://doi.org/10.1112/s0024610798006681" @default.
- W1985497716 hasPublicationYear "1998" @default.
- W1985497716 type Work @default.
- W1985497716 sameAs 1985497716 @default.
- W1985497716 citedByCount "2" @default.
- W1985497716 countsByYear W19854977162019 @default.
- W1985497716 crossrefType "journal-article" @default.
- W1985497716 hasAuthorship W1985497716A5037053721 @default.
- W1985497716 hasAuthorship W1985497716A5081865508 @default.
- W1985497716 hasBestOaLocation W19854977161 @default.
- W1985497716 hasConcept C104114177 @default.
- W1985497716 hasConcept C114614502 @default.
- W1985497716 hasConcept C121332964 @default.
- W1985497716 hasConcept C132459708 @default.
- W1985497716 hasConcept C134306372 @default.
- W1985497716 hasConcept C137800194 @default.
- W1985497716 hasConcept C14036430 @default.
- W1985497716 hasConcept C18903297 @default.
- W1985497716 hasConcept C2524010 @default.
- W1985497716 hasConcept C2777299769 @default.
- W1985497716 hasConcept C2777759810 @default.
- W1985497716 hasConcept C2834757 @default.
- W1985497716 hasConcept C33923547 @default.
- W1985497716 hasConcept C46757340 @default.
- W1985497716 hasConcept C53051483 @default.
- W1985497716 hasConcept C74650414 @default.
- W1985497716 hasConcept C78458016 @default.
- W1985497716 hasConcept C86803240 @default.
- W1985497716 hasConceptScore W1985497716C104114177 @default.
- W1985497716 hasConceptScore W1985497716C114614502 @default.
- W1985497716 hasConceptScore W1985497716C121332964 @default.
- W1985497716 hasConceptScore W1985497716C132459708 @default.
- W1985497716 hasConceptScore W1985497716C134306372 @default.
- W1985497716 hasConceptScore W1985497716C137800194 @default.
- W1985497716 hasConceptScore W1985497716C14036430 @default.
- W1985497716 hasConceptScore W1985497716C18903297 @default.
- W1985497716 hasConceptScore W1985497716C2524010 @default.
- W1985497716 hasConceptScore W1985497716C2777299769 @default.
- W1985497716 hasConceptScore W1985497716C2777759810 @default.
- W1985497716 hasConceptScore W1985497716C2834757 @default.
- W1985497716 hasConceptScore W1985497716C33923547 @default.
- W1985497716 hasConceptScore W1985497716C46757340 @default.
- W1985497716 hasConceptScore W1985497716C53051483 @default.
- W1985497716 hasConceptScore W1985497716C74650414 @default.
- W1985497716 hasConceptScore W1985497716C78458016 @default.
- W1985497716 hasConceptScore W1985497716C86803240 @default.
- W1985497716 hasIssue "2" @default.
- W1985497716 hasLocation W19854977161 @default.
- W1985497716 hasOpenAccess W1985497716 @default.
- W1985497716 hasPrimaryLocation W19854977161 @default.
- W1985497716 hasRelatedWork W1976332093 @default.
- W1985497716 hasRelatedWork W2061089925 @default.
- W1985497716 hasRelatedWork W2105594625 @default.
- W1985497716 hasRelatedWork W2145422818 @default.
- W1985497716 hasRelatedWork W2167211785 @default.
- W1985497716 hasRelatedWork W2168645698 @default.
- W1985497716 hasRelatedWork W2199409340 @default.
- W1985497716 hasRelatedWork W2593911140 @default.
- W1985497716 hasRelatedWork W3046916520 @default.
- W1985497716 hasRelatedWork W4301079940 @default.
- W1985497716 hasVolume "58" @default.
- W1985497716 isParatext "false" @default.
- W1985497716 isRetracted "false" @default.
- W1985497716 magId "1985497716" @default.
- W1985497716 workType "article" @default.