## Banach Journal of Mathematical Analysis

### $\ell_{p}$-maximal regularity for a class of fractional difference equations on UMD spaces: The case $1\lt \alpha\leq2$

#### Abstract

By using Blunck’s operator-valued Fourier multiplier theorem, we completely characterize the existence and uniqueness of solutions in Lebesgue sequence spaces for a discrete version of the Cauchy problem with fractional order $1\lt \alpha\leq2$. This characterization is given solely in spectral terms on the data of the problem, whenever the underlying Banach space belongs to the UMD-class.

#### Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 188-206.

Dates
Accepted: 11 March 2016
First available in Project Euclid: 30 November 2016

https://projecteuclid.org/euclid.bjma/1480474819

Digital Object Identifier
doi:10.1215/17358787-3784616

Mathematical Reviews number (MathSciNet)
MR3577375

Zentralblatt MATH identifier
1359.39003

#### Citation

Lizama, Carlos; Murillo-Arcila, Marina. $\ell_{p}$ -maximal regularity for a class of fractional difference equations on UMD spaces: The case $1\lt \alpha\leq2$. Banach J. Math. Anal. 11 (2017), no. 1, 188--206. doi:10.1215/17358787-3784616. https://projecteuclid.org/euclid.bjma/1480474819

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