Grand Triebel-Lizorkin-Morrey spaces

Abstract

This article studies the Triebel-Lizorkin-type spaces built on grand Morrey spaces on Euclidean spaces. We establish a number of characterizations on the grand Triebel-Lizorkin-Morrey spaces such as the Peetre maximal function characterizations, the Lusin area function characterizations, and the gλ∗{g}_{\lambda }^{\ast } function characterizations. The boundedness of the Fourier multipliers on the grand Triebel-Lizorkin-Morrey spaces is also obtained.

Keywords

• grand lebesgue spaces
• morrey spaces
• triebel-lizorkin spaces
• fourier multiplier
• 42b20
• 42b30
• 42b35
• 46e30