Old and New Morrey Spaces with Heat Kernel Bounds |
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Authors: | Xuan Thinh Duong Jie Xiao Lixin Yan |
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Institution: | (1) Department of Mathematics, MacQuarie University, NSW 2109, Australia;(2) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada;(3) Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China |
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Abstract: | Given p ∈ 1,∞) and λ ∈ (0, n), we study Morrey space
of all locally integrable complex-valued functions f on
such that for every open Euclidean ball B ⊂
with radius rB there are numbers C = C(f ) (depending on f ) and c = c(f,B) (relying upon f and B) satisfying
and derive old and new, two essentially different cases arising from either choosing
or replacing c by
—where tB is scaled to rB and pt(·, ·) is the kernel of the infinitesimal generator L of an analytic semigroup
on
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. |
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Keywords: | |
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