Function Spaces and Inequalities by Pankaj Jain & Hans-Jürgen Schmeisser

Author:Pankaj Jain & Hans-Jürgen Schmeisser
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

Please note that for the function does not have any moment condition. If not otherwise stated, we define for a function the dyadic dilates by for and any . We remark that is not covered by the construction above because it is usually realized with a different function which has different properties compared to .

2.1 Besov and Triebel-Lizorkin Spaces with Variable Exponents

Here we introduce the spaces which we are interested in. We study Besov and Triebel-Lizorkin spaces with variable integrability and variable smoothness. We take advantage of the concept of admissible weight sequences to define the variable smoothness.

Definition 1

For fixed real numbers and the class of admissible weights is the collection of all positive weight sequences on with:(i)There exists a constant such that for fixed and arbitrary

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