1,377 research outputs found
Natural maps between CAT(0) boundaries
It is shown that certain natural maps between the ideal, Gromov, and end
boundaries of a complete CAT(0) space can fail to be either injective or
surjective. Additionally the natural map from the Gromov boundary to the end
boundary of a complete CAT(-1) space can fail to be either injective or
surjective.Comment: 8 page
Rough CAT(0) spaces
We investigate various notions of rough CAT(0). These conditions define
classes of spaces that strictly include the union of all Gromov hyperbolic
length spaces and all CAT(0) spaces.Comment: Corrected typos and updated Corollaries 3.22 and 3.2
Sobolev spaces: a short course
Notes for a course in Sobolev spaces given to the Department of Mathematical Analysis, University of La Laguna, Tenerife in May 2000
Pointwise multipliers for reverse Hölder spaces II
We classify weights which map strong reverse Hölder weight classes to weak reverse Hölder weight spaces under pointwise multiplication
Slice conditions and their applications
Slice-type conditions and their relatives have been used in a number of papers of the author and various collaborators to investigate a variety of problems in analysis
including Sobolev-type imbedding theorems ([BuKo], [BuOS], [BuSt1], [Bu]), quasiconformal equivalence of domains ([BuSt2], [Bu]), and Gromov hyperbolicity ([BaBu]). Despite their usefulness, these conditions are still somewhat mysterious, but some recent research has helped to shed more light on them ([BaBu], [BuSt3], [BuDiSt]).
There are quite a few varieties of slice conditions, partially reflecting the fact that different applications require dierent conditions. In this paper, we define
some of these variants, discuss how they differ from each other, and summarize their applications. Along the way, we encounter quite a few examples, counterexamples, and open questions. We discuss (strong) slice conditions and Gromov hyperbolicity in Section 2, weak slice conditions and their applications in Section 3, and some examples and useful lemmas in Section 4
Sequences of reverse Minkowski type
We study sequences of positive numbers satisfying a reverse Minkowski condition. In particular, we classify those monotonic decreasing sequences which can be rearranged to satisfy such a condition
Mixed norms and analytic function spaces
We dene and investigate general mixed-norm type sequence spaces, and strengthen inequalities of Hardy-Littlewood, Hausdor-Young, and others
Space-filling curves and related functions
In this paper, we shall investigate several questions related to space-lling curves. We start with a question whose answer has been known (although not widely known, it would appear) for rather a long time
Space-filling curves and related functions
In this paper, we shall investigate several questions related to space-lling curves. We start with a question whose answer has been known (although not widely known, it would appear) for rather a long time
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