Uniform continuity of nonautonomous superposition operators in ΛBV-spaces
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Jacek Gulgowski
Abstract
In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded Λ-variation. In particular, we give the sufficient conditions for nonautonomous superposition operators to continuously map a space of functions of bounded Λ-variation into itself. The conditions cover the generators being functions of
References
[1] J. Appell, J. Banaś and N. Merentes, Bounded Variation and Around, De Gruyter Ser. Nonlinear Anal. Appl. 17, De Gruyter, Berlin, 2014. 10.1515/9783110265118Search in Google Scholar
[2] D. Bugajewska, D. Bugajewski, P. Kasprzak and P. Maćkowiak, Nonautonomous superposition operators in the spaces of functions of bounded variation, Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 637–660. 10.12775/TMNA.2016.070Search in Google Scholar
[3]
D. Bugajewski, K. Czudek, J. Gulgowski and J. E. Sadowski,
On some nonlinear operators in
[4] D. Bugajewski, J. Gulgowski and P. Kasprzak, On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation, Ann. Mat. Pura Appl. (4) 195 (2016), no. 5, 1513–1530. 10.1007/s10231-015-0526-7Search in Google Scholar
[5] K. Czudek, Bernstein and Kantorovich polynomials diminish the Λ-variation, J. Math. Anal. Appl. 452 (2017), no. 2, 912–925. 10.1016/j.jmaa.2017.03.035Search in Google Scholar
[6] E. Hille, Methods in Classical and Functional Analysis, Addison-Wesley, Reading, 1972. Search in Google Scholar
[7]
P. Kasprzak and P. Maćkowiak,
Local boundedness of nonautonomous superposition operators in
[8] P. Maćkowiak, On the continuity of superposition operators in the space of functions of bounded variation, Aequationes Math. 91 (2017), no. 4, 759–777. 10.1007/s00010-017-0491-xSearch in Google Scholar
[9] G. A. Monteiro, On functions of bounded semivariation, Real Anal. Exchange 40 (2014/15), no. 2, 233–276. 10.14321/realanalexch.40.2.0233Search in Google Scholar
[10] F. Prus-Wiśniowski, Separability of the space of continuous functions that are continuous in Λ-variation, J. Math. Anal. Appl. 344 (2008), no. 1, 274–291. 10.1016/j.jmaa.2008.02.014Search in Google Scholar
[11] F. Prus-Wiśniowski, Λ-absolute continuity, Rocky Mountain J. Math. 39 (2009), no. 5, 1613–1656. 10.1216/RMJ-2009-39-5-1613Search in Google Scholar
[12] D. Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. 10.4064/sm-44-2-107-117Search in Google Scholar
[13] D. Waterman, On L-bounded variation, Studia Math. 57 (1976), no. 1, 33–45. 10.4064/sm-57-1-33-45Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics
- Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
- Variable weak Hardy spaces WHLp(·)(ℝn) associated with operators satisfying Davies–Gaffney estimates
- Sublinear operators on weighted Hardy spaces with variable exponents
- Hereditarily minimal topological groups
- Rational torsion of generalized Jacobians of modular and Drinfeld modular curves
- Morita homotopy theory for (∞,1)-categories and ∞-operads
- Homomorphisms into totally disconnected, locally compact groups with dense image
- On the Ramanujan–Petersson conjecture for modular forms of half-integral weight
- Uniform continuity of nonautonomous superposition operators in ΛBV-spaces
- Simple modules over the Lie algebras of divergence zero vector fields on a torus
- Effective bounds for the Andrews spt-function
- Free subgroups in k(x1,... ,xn)(X;σ) and k(x,y)(k;σ)
- A geometric proof of an equivariant Pieri rule for flag manifolds
- On relations between weak and strong type inequalities for modified maximal operators on non-doubling metric measure spaces
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Articles in the same Issue
- Frontmatter
- Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics
- Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
- Variable weak Hardy spaces WHLp(·)(ℝn) associated with operators satisfying Davies–Gaffney estimates
- Sublinear operators on weighted Hardy spaces with variable exponents
- Hereditarily minimal topological groups
- Rational torsion of generalized Jacobians of modular and Drinfeld modular curves
- Morita homotopy theory for (∞,1)-categories and ∞-operads
- Homomorphisms into totally disconnected, locally compact groups with dense image
- On the Ramanujan–Petersson conjecture for modular forms of half-integral weight
- Uniform continuity of nonautonomous superposition operators in ΛBV-spaces
- Simple modules over the Lie algebras of divergence zero vector fields on a torus
- Effective bounds for the Andrews spt-function
- Free subgroups in k(x1,... ,xn)(X;σ) and k(x,y)(k;σ)
- A geometric proof of an equivariant Pieri rule for flag manifolds
- On relations between weak and strong type inequalities for modified maximal operators on non-doubling metric measure spaces
-
Global well-posedness and temporal decay estimates to the fractional Cahn–Hilliard equation in
