Mathematical Journal of Okayama University 61巻 1号
2019-01 発行

Complex interpolation of smoothness Triebel-Lizorkin-Morrey spaces

Hakim, Denny Ivanal Department of Mathematics and Information Sciences, Tokyo Metropolitan University
Nogayama, Toru Department of Mathematics and Information Sciences, Tokyo Metropolitan University
Sawano, Yoshihiro Department of Mathematics and Information Sciences, Tokyo Metropolitan University
Publication Date
2019-01
Abstract
This paper extends the result in [8] to Triebel-Lizorkin-Morrey spaces which contains 4 parameters p, q, r, s. This paper reinforces our earlier paper [8] by Nakamura, the first and the third authors in two different directions. First, we include the smoothness parameter s and the second smoothness parameter r. In [8] we assumed s = 0 and r = 2. Here we relax the conditions on s and r to s ∈ R and 1 < r ≤ ∞. Second, we apply a formula obtained by Bergh in 1978 to prove our main theorem without using the underlying sequence spaces.
Keywords
smoothness Morrey spaces
Triebel-Lizorkin-Morrey spaces
complex interpolation
square function
Comments
Mathematics Subject Classification. Primary 42B35; Secondary 41A17, 26B33.