Inclusion relations between LP-Sobolev and Wiener amalgam spaces

We determined optimal inclusion relations between L-P-Sobolev and Wiener amalgam spaces. For applications, we discuss mapping properties of unimodular Fourier multipliers e(i vertical bar D vertical bar alpha) between L-P-Sobolev and Wiener amalgam spaces and derive some Littlewood-Paley type inequalities. (C) 2014 Elsevier Inc. All rights reserved.