Annals of Functional Analysis

On multipliers between bounded variation spaces

Héctor Camilo Chaparro

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Wiener-type variation spaces, also known as BVp-spaces (1p<), are complete normed linear spaces. A function g is called a multiplier from BVp to BVq if the pointwise multiplication fg belongs to BVq for each fBVp. In this article, we characterize the multipliers from BVp to BVq for the cases 1q<p and 1pq.

Article information

Ann. Funct. Anal., Volume 9, Number 3 (2018), 376-383.

Received: 21 June 2017
Accepted: 25 July 2017
First available in Project Euclid: 6 February 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B38: Operators on function spaces (general)
Secondary: 26A45: Functions of bounded variation, generalizations

multipliers multiplication operator bounded variation


Chaparro, Héctor Camilo. On multipliers between bounded variation spaces. Ann. Funct. Anal. 9 (2018), no. 3, 376--383. doi:10.1215/20088752-2017-0047.

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  • [1] J. Appell, J. Banaś, and N. Merentes, Bounded Variation and Around, de Gruyter Ser. Nonlinear Anal. Appl. 17, de Gruyter, Berlin, 2014.
  • [2] F. R. Astudillo-Villalba and J. C. Ramos-Fernández, Multiplication operators on the space of functions of bounded variation, Demonstratio Math. 50 (2017), no. 1, 105–115.
  • [3] S. Barza and M. Lind, A new variational characterization of Sobolev spaces, J. Geom. Anal. 25 (2015), no. 4, 2185–2195.
  • [4] R. E. Castillo and H. C. Chaparro, Weighted composition operator on two-dimensional Lorentz spaces, Math. Inequal. Appl. 20 (2017), no. 3, 773–799.
  • [5] R. E. Castillo, H. C. Chaparro, and J. C. Ramos-Fernández, Orlicz-Lorentz spaces and their multiplication operators, Hacet. J. Math. Stat. 44 (2015), no. 5, 991–1009.
  • [6] C. Jordan, Sur la série de Fourier, C. R. Math. Acad. Sci. Paris 92 (1881), no. 5, 228–230.
  • [7] R. Kantrowitz, Submultiplicativity of norms for spaces of generalized $\mathit{BV}$-functions, Real Anal. Exchange 36 (2010/2011), no. 1, 169–175.
  • [8] J. Malý, Absolutely continuous functions of several variables, J. Math. Anal. Appl. 231 (1999), no. 2, 492–508.
  • [9] E. Nakai, Pointwise multipliers on the Lorentz spaces, Mem. Osaka Kyoiku Univ. Ser. III Nat. Sci. Appl. Sci. 45 (1996), no. 1, 1–7.
  • [10] J. C. Ramos-Fernández, Some properties of multiplication operators acting on Banach spaces of measurable functions, Bol. Mat. (N.S.) 23 (2016), no. 2, 221–237.
  • [11] H. Takagi and K. Yokouchi, “Multiplication and composition operators between two $L^{p}$-spaces” in Function Spaces (Edwardsville, Ill., 1998), Contemp. Math. 232, Amer. Math. Soc., Providence, 1999, 321–338.
  • [12] N. Wiener, The quadratic variation of a function and its Fourier coefficients, Stud. Appl. Math. 3 (1924), no. 2, 72–94.