Gagliardo-Nirenberg inequality through a brand new pointwise estimate
Authors: Karol Lesnik, Tomas Roskovec, Filip Soudsky
Summary: We show a brand new sort of pointwise estimate of the Kalamajska-Mazya-Shaposhnikova sort, the place sparse averaging operators exchange the maximal operator. It permits us to increase the Gagliardo-Nirenberg interpolation inequality to all rearrangement invariant Banach perform areas with none assumptions on their higher Boyd index, i.e. omitting issues attributable to unboundedness of maximal operator on areas near L1. Particularly, we take away pointless assumptions from the Gagliardo-Nirenberg inequality within the setting of Orlicz and Lorentz areas. The utilized methodology is new on this context and could also be seen as a sort of sparse domination method fitted to the context of rearrangement invariant Banach perform areas.
