Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences

作者：Kempka Henning^*; Vybiral Jan

来源：Journal of Fourier Analysis and Applications, 2012, 18(4): 852-891.

DOI：10.1007/s00041-012-9224-7

• Besov spaces
• Triebel-Lizorkin spaces
• Variable smoothness
• Variable integrability
• Ball means of differences
• Peetre maximal operator
• 2-microlocal spaces

We study the spaces and of Besov and Triebel-Lizorkin type as introduced recently in Almeida and Hasto (J. Funct. Anal. 258(5):1628-2655, 2010) and Diening et al. (J. Funct. Anal. 256(6):1731-1768, 2009). Both scales cover many classical spaces with fixed exponents as well as function spaces of variable smoothness and function spaces of variable integrability. %26lt;br%26gt;The spaces and have been introduced in Almeida and Hasto (J. Funct. Anal. 258(5):1628-2655, 2010) and Diening et al. (J. Funct. Anal. 256(6):1731-1768, 2009) by Fourier analytical tools, as the decomposition of unity. Surprisingly, our main result states that these spaces also allow a characterization in the time-domain with the help of classical ball means of differences. %26lt;br%26gt;To that end, we first prove a local means characterization for with the help of the so-called Peetre maximal functions. Our results do also hold for 2-microlocal function spaces and which are a slight generalization of generalized smoothness spaces and spaces of variable smoothness.

• 出版日期2012-8