On functions of bounded Λ-variation and integral smoothness

Lind, Martin

doi:10.1515/forum-2012-0186

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Introduction and Main Results1

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Cited by 5 publications

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“…For more detailed results on this topic, we refer readers to [4,9,10,[14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Estimates ofLpModulus of Continuity of Generalized Bounded Variation Classes

Wang

Wu²

2014

Journal of Function Spaces

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Some sharp estimates of the(1 ≤ < ∞) modulus of continuity of classes of Λ -bounded variation are obtained. As direct applications, we obtain estimates of order of Fourier coefficients of functions of Λ -bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relations ⊂ Λ . Our results include the corresponding known results of the class Λ as a special case.2 Journal of Function Spaces and nondecreasing function ( ) on [0, ∞) such that ( ) ≡ 1 , 0 ≤ ≤ 1 and ( ) = , = 1, 2, . . ., then we say that ( ) generates Λ. By the nondecreasing property of Λ, it is easily verified that if ( ) generates Λ, then Submit your manuscripts at

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“…For more detailed results on this topic, we refer readers to [4,9,10,[14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Estimates ofLpModulus of Continuity of Generalized Bounded Variation Classes

Wang

Wu²

2014

Journal of Function Spaces

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“…When p = 1, ΛBV (p) is the well-known Waterman space ΛBV (see e. g. [25] and [26]). Some of the properties and applications of functions of class ΛBV (p) were discussed in [8], [9], [11], [12], [16], [17], [18], [19], [20], [22], [23] and [24]. ΛBV (p) equipped with the norm f Λ, p := |f (0)| + V (f ) is a Banach space.…”

mentioning

confidence: 99%