Embedding of classes of functions with bounded $${\Phi}$$ Φ -variation into generalized Lipschitz spaces

Wu, Xuezhi

doi:10.1007/s10474-016-0656-4

Cited by 6 publications

(4 citation statements)

References 13 publications

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“…Each year topics related to variation are gaining more and more popularity among mathematicians (see, for examples, the recent papers [10,19,21] concerning the Schramm variation, or the general monographs [1,17]).…”

mentioning

confidence: 99%

On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

Bugajewski¹,

Gulgowski²,

Kasprzak³

2016

Journal of Mathematical Analysis and Applications

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mentioning

confidence: 99%

On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

Bugajewski¹,

Gulgowski²,

Kasprzak³

2016

Journal of Mathematical Analysis and Applications

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“…where C is a positive constant depending solely on f . In the course of the proof of Theorem 2.1 in [25], the author proceeds to estimate ( n j=1 x q j ) 1 q under the restriction…”

Section: Proofs Of Main Resultsmentioning

confidence: 99%

Relations between Schramm spaces and generalized Wiener classes

Goodarzi

Hormozi

Memić

2017

Journal of Mathematical Analysis and Applications

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“…3 The following lemma will be used in the proof of the sufficiency part of Theorem 6.2. This was first proven in [29]. For each n, −1 n (x) denotes the inverse of the function n (x) := The proof of the following result uses techniques form [17] and [18].…”

Section: Embedding Schramm Spaces Into V P [ ]mentioning

confidence: 99%

The Modulus of p-Variation and Its Applications

Esslamzadeh

Goodarzi

Hormozi

et al. 2021

J Fourier Anal Appl

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Let ν be a nondecreasing concave sequence of positive real numbers and 1 ≤ p < ∞. In this note, we introduce the notion of modulus of p-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain K -functionals. Using this new tool, we first define a Banach space, denoted V p [ν], that is a natural unification of the Wiener class BV p and the Chanturiya class V [ν]. Then we prove that V p [ν] satisfies a Helly-type selection principle which enables us to characterize continuous functions in V p [ν] in terms of their Fejér means. We also prove that a certain K -functional for the couple (C, BV p ) can be expressed in terms of the modulus of p-variation, where C denotes the space of continuous functions. Next, we obtain equivalent optimal conditions for the uniform convergence of the Fourier series of all functions in each of the classes C ∩ V p [ν] andwhere ω is a modulus of continuity and H ω denotes its associated Lipschitz class. Finally, we establish sharp embeddings into V p [ν] of various spaces of functions of generalized bounded variation. As a by-product of these latter results, we infer embedding results for certain symmetric sequence spaces.Communicated by Sergij Tikhonov.

show abstract

Embedding of classes of functions with bounded $${\Phi}$$ Φ -variation into generalized Lipschitz spaces

Cited by 6 publications

References 13 publications

On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

Relations between Schramm spaces and generalized Wiener classes

The Modulus of p-Variation and Its Applications

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