Aug 2026· Canadian mathematical bulletin· 1 citation· 17 references
Mathematics
Abstract
We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in other words, the optimal Orlicz domain is automatically the optimal r.i. domain. More generally, we show that every Luxemburg–Orlicz norm is equivalent to a sublinear functional which makes more computable a certain expression for a dual norm arising in the
K
$\mathcal {K}$
script upper K
-theory of interpolation. As applications, we obtain Orlicz space mapping properties for the Hardy–Littlewood maximal function, approximate identities, and Calderón–Zygmund singular integral operators. These mapping properties are shown to be optimal for the Hardy–Littlewood maximal function and the approximate identities.
In this paper, we shed light on basic questions such as: What is the"right"underlying set on which a function space lives, and is this set uniquely determined? What are the appropriate morphisms to classify function spaces? When does a weighted composition operator induce an isomorphism, and when does it induce an isom...
We introduce a class of plurisubharmonic weights on \mathbb C^n and develop a theory of the associated weighted Fock spaces F_\varphi^p. The curvature assumptions are imposed on a \mathcal C^2-regularization at bounded distance from the original weight. Thus the original weight need not be smooth or strictly plurisubha...
Given a complete doubling metric measure space $(X,\rho,\mu)$ supporting a Poincar\'e inequality, we prove weak-type characterizations of the Sobolev space $\dot{W}^{1,p}(\mu)$ and the space of functions of bounded variation, achieving a full analogy in general Poincar\'e spaces with the Euclidean results of Brezis et...
T. Hytönen, Da-Chun Yang, Wen Yuan et al.· 2 citations
In this work, we establish a strong factorization for Hardy-Orlicz spaces on the upper half-plane. We show that the product of two functions belonging respectively to Hardy-Orlicz spaces $H^{\Phi_{1}}$ and $H^{\Phi_{2}}$ lies in a third space $H^{\Phi_{3}}$, and every holomorphic function in $H^{\Phi_{3}}$ admits such...
Trace spaces determine exactly which initial values are compatible with an evolution class. We identify the exact trace generated by vector-valued Morrey control in time and show that it differs essentially from the classical $L^p$ theory. For a Banach couple $X_1\hookrightarrow X_0$, the trace of the natural Morrey ev...
In this paper, we extend a large part of the uniformization theory of Bonk-Heinonen-Koskela [Asterisque 2001] to length spaces that are not necessarily proper or geodesic. Among other things, we show that there is a one-to-one correspondence between the quasiisometry classes of complete roughly starlike Gromov hyperbol...
Shuliang Gao, Chang-Yu Guo, Miao He· 0 citations
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