caa a22 4500 463246748 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00041-006-6057-2 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6057-2 Old and New Morrey Spaces with Heat Kernel Bounds [Elektronische Daten] [Xuan Thinh Duong, Jie Xiao, Lixin Yan] Given p ∈ [1,∞) and λ ∈ (0, n), we study Morrey space $L^{p,\lambda}({\Bbb R}^n)$ of all locally integrable complex-valued functions f on ${\Bbb R}^n$ such that for every open Euclidean ball B ⊂ ${\Bbb R}^n$ with radius rB there are numbers C = C(f ) (depending on f ) and c = c(f,B) (relying upon f and B) satisfying $r^{-\lambda}_B\sum_B \vert f(x) -c\vert^p dx\leq C$ and derive old and new, two essentially different cases arising from either choosing $c = f_B = \vert B\vert^{−1} \sum_B f (y)dy$ or replacing c by $P_{t_B} (x) = \sum_{t_B} p_{t_B} (x, y)f (y) dy$ —where tB is scaled to rB and pt(·, ·) is the kernel of the infinitesimal generator L of an analytic semigroup $\{e^{−tL}\}_{t\geq 0}$ on $L^2({\Bbb R}^n).$ 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. Birkhauser Boston, 2006 Duong Xuan Thinh Department of Mathematics, MacQuarie University, NSW 2109, Australia aut Xiao Jie Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada aut Yan Lixin Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/1(2007-02-01), 87-111 1069-5869 13:1<87 2007 13 41 https://doi.org/10.1007/s00041-006-6057-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6057-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Duong Xuan Thinh Department of Mathematics, MacQuarie University, NSW 2109, Australia aut NATIONALLICENCE 700 1- Xiao Jie Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada aut NATIONALLICENCE 700 1- Yan Lixin Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/1(2007-02-01), 87-111 1069-5869 13:1<87 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer