In this dissertation the action of maximal operators and the properties of oscillating functions are studied in the context of doubling measure spaces. The work consists of four articles, in which boundedness of maximal operators is studied in several function spaces and different aspects of the oscillation of functions are considered. In particular, new characterizations for the BMO and the weak L∞ are obtained.
|Translated title of the contribution||Boundedness of maximal operators and oscillation of functions in metric measure spaces|
|Publication status||Published - 2010|
|MoE publication type||G5 Doctoral dissertation (article)|
- doubling measure
- maximal functions
- discrete convolution
- John-Nirenberg inequality