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2. On Denjoy type extensions of the Pettis integral
- Creator:
- Naralenkov, Kirill
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- scalar derivative, approximate scalar derivative, absolute continuity, bounded variation, $VBG$ function, $ACG$ function, Pettis integral, and Denjoy-Pettis integral
- Language:
- English
- Description:
- In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. On the regularity of the one-sided Hardy-Littlewood maximal functions
- Creator:
- Liu, Feng and Mao, Suzhen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Sobolevův prostor, ohraničená variace, kontinuita, one-sided maximal operator, Sobolev space, bounded variation, continuity, 13, and 51
- Language:
- English
- Description:
- In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators M+ and M−. More precisely, we prove that M+ and M− map W¹,p(R) → W1,p(R) with 1 < p < nekonečno, boundedly and continuously. In addition, we show that the discrete versions M+ and M− map BV(ℤ) → BV(ℤ) boundedly and map l¹(ℤ) → BV(ℤ) continuously. Specially, we obtain the sharp variation inequalities of M+ and M−, that is Var(M+(f))<Var(f) and Var(M−(f))<Var(f) if f ∈ BV(ℤ), where Var(f) is the total variation of f on ℤ and BV(ℤ) is the set of all functions f: ℤ → R satisfying Var(f) < nekonečno., Feng Liu, Suzhen Mao., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. On vector functions of bounded convexity
- Creator:
- Veselý, Libor and Zajíček, Luděk
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- bounded convexity, delta-convex mapping, bounded variation, and Banach space
- Language:
- English
- Description:
- Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity Kb a F is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. The dual of the space of functions of bounded variation
- Creator:
- Aye, Khaing Khaing and Lee, Peng Yee
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- bounded variation, two-norm space, dual space, linear functional, Henstock integral, Stieltjes integral, and regulated function
- Language:
- English
- Description:
- In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public