Mathematics – Analysis of PDEs
Scientific paper
2006-10-02
Mathematics
Analysis of PDEs
Scientific paper
Given $p\in [1,\infty)$ and $\lambda\in (0,n)$, we study Morrey space ${\rm L}^{p,\lambda}({\mathbb R}^n)$ of all locally integrable complex-valued functions $f$ on ${\mathbb R}^n$ such that for every open Euclidean ball $B\subset{\mathbb R}^n$ with radius $r_B$ there are numbers $C=C(f)$ (depending on $f$) and $c=c(f,B)$ (relying upon $f$ and $B$) satisfying $$ r_B^{-\lambda}\int_{B}|f(x)-c|^pdx\le C $$ and derive old and new, two essentially different cases arising from either choosing $c=f_B=|B|^{-1}\int_{B}f(y)dy$ or replacing $c$ by $P_{t_B}(x)=\int_{t_B}p_{t_B}(x,y)f(y)dy$ -- where $t_B$ is scaled to $r_B$ and $p_t(\cdot,\cdot)$ is the kernel of the infinitesimal generator $L$ of an analytic semigroup $\{e^{-tL}\}_{t\ge0}$ on ${\rm L}^2({\mathbb R}^n)$. Consequently, we are led to simultaneously characterize the old and new Morrey spaces, but also to show that for a suitable operator $L$, the new Morrey space is equivalent to the old one.
Duong X.
Xiao Jiang
Yan Lihong
No associations
LandOfFree
Old and New Morry Spaces via Heat Kernel Bounds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Old and New Morry Spaces via Heat Kernel Bounds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Old and New Morry Spaces via Heat Kernel Bounds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-176385