The continuous primitive integral in the plane

zbMath1451.26013arXiv1906.11789MaRDI QIDQ785249

Erik O.Talvila

Publication date: 6 August 2020

Published in: Real Analysis Exchange (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.11789

zbMATH Keywords

distributionBanach algebraconvolutionBanach latticedual spaceHenstock-Kurzweil integralHölder inequalityintegration by partsHardy-Krause variationcontinuous primitive integralAlexiewicz norm

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Integration of real functions of several variables: length, area, volume (26B15) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (2)

The double Fourier transform of non-Lebesgue integrable functions of bounded Hardy-Krause variation ⋮ Solving Poisson equation by distributional HK-integral: prospects and limitations

Cites Work

• The use of an isometric isomorphism on the completion of the space of Henstock-Kurzweil integrable functions
• On singular nonlinear distributional and impulsive initial and boundary value problems
• Fourier series with the continuous primitive integral
• On the solvability of distributional and impulsive systems of Cauchy problems
• On first-order periodic boundary value problems and distributional Henstock-Kurzweil integrals
• The regulated primitive integral
• On nonlinear distributional and impulsive Cauchy problems
• The distributional Denjoy integral
• Convolutions with the continuous primitive integral
• Topology for the spaces of Denjoy integrable functions
• The space of Henstock integrable functions of two variables
• A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral
• On the Alexiewicz topology of the Denjoy space
• On the Denjoy-Perron-Henstock-Kurzweil integral
• The one-dimensional heat equation in the Alexiewicz norm
• Harmonic Function Theory
• Integrals and Banach spaces for finite order distributions
• On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil
• A Course in Commutative Banach Algebras
• The Divergence Theorem
• An integral defined by approximating $BV$ partitions of unity
• A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
• On Definitions of Bounded Variation for Functions of Two Variables
• Kurzweil–Stieltjes Integral
• The L p primitive integral
• Bounded Variation and Around
• Linear functionals on Denjoy-integrable functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The continuous primitive integral in the plane