Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 4 (2017), 713-743.
Fourier multiplier theorems on Besov spaces under type and cotype conditions
In this article, we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents and , which depend on the type and cotype of the underlying Banach spaces. In a previous article, we considered - multiplier theorems. In the current article, we show that in the Besov scale one can obtain results with optimal integrability exponents. Moreover, we derive a sharp result in the - setting as well.
We consider operator-valued multipliers without smoothness assumptions. The results are based on a Fourier multiplier theorem for functions with compact Fourier support. If the multiplier has smoothness properties, then the boundedness of the multiplier operator extrapolates to other values of and for which remains constant.
Banach J. Math. Anal., Volume 11, Number 4 (2017), 713-743.
Received: 10 June 2016
Accepted: 12 October 2016
First available in Project Euclid: 18 May 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42B15: Multipliers
Secondary: 42B35: Function spaces arising in harmonic analysis 46B20: Geometry and structure of normed linear spaces 46E40: Spaces of vector- and operator-valued functions 47B38: Operators on function spaces (general)
Rozendaal, Jan; Veraar, Mark. Fourier multiplier theorems on Besov spaces under type and cotype conditions. Banach J. Math. Anal. 11 (2017), no. 4, 713--743. doi:10.1215/17358787-2017-0011. https://projecteuclid.org/euclid.bjma/1495094417