Timo Takala (Aalto University)

Title: An introduction to John-Nirenberg spaces and recent results featuring vanishing subspaces and maximal functions

Abstract: The space of functions of bounded mean oscillation BMO was first defined by John and Nirenberg in 1961, and it is an essential function space in harmonic analysis. The John-Nirenberg space JNp was first defined in the same paper and it is also related to oscillations, but it has not been studied as much as BMO. In this talk I will first present the definition and some of

the basic properties of JNp functions.

The spaces VMO and CMO are well-known vanishing subspaces of BMO. Corresponding vanishing subspaces of JNp have been defined and studied recently and some characterizations for those vanishing subspaces have been developed. Another active line of research involves studying the regularity of (fractional) maximal functions of various types of functions. In the talk I will present some recent results about JNp functions, the vanishing subspaces of JNp, and the (fractional) maximal functions of BMO, VMO and JNp functions.

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Meeting ID: 825 9962 4658

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