Add to ORKGThis paper is concerned with defining Lipschitz spaces on Σn-1 the surface of the unit sphere in Rn. The importance of this example is that Σn-1 is not a group but a symmetric space. One begins with functions in Lp(Σn-1),1≤p≤∞. Σn-1 is a symmetric space and is related in a natural way to the rotation group SO(n). One can then use the group SO(n) to define first and second differences for functions in Lp(Σn-1). Such a function is the boundary value of its Poisson integral. This enables one to work with functions which are harmonic. Differences can then be replaced by derivatives
By taking an appropriate zero-curvature limit, we obtain the spherical functions on flat symmetric s...
In the setting of a metric measure space (X, d, µ) with an n-dimensional Radon measure µ, we give a ...
First published in the Bulletin of the American Mathematical Society in Vol.74, 1968, published by t...
This paper is concerned with defining Lipschitz spaces on Σn-1 the surface of the unit sphere in Rn....
In this paper Lipschitz spaces of distributions are defined and various inclusion relations are show...
In this paper the equivalence between the Campanato spaces and homogeneous Lipschitz spaces is shown...
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S...
AbstractFunction spaces of Hardy–Sobolev–Besov type on symmetric spaces of noncompact type and unimo...
The main objective of this work is to develop a theory of Hardy spaces on the surface (SIGMA)(,N) of...
summary:We present explicit expressions of the Poisson kernels for geodesic balls in the higher dime...
We determine precise conditions for the boundedness of Bergman projections from Lebesgue classes ont...
AbstractWe use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions...
summary:If the Poisson integral of the unit disc is replaced by its square root, it is known that no...
AbstractWe continue a program to develop layer potential techniques for PDE on Lipschitz domains in ...
Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α...
By taking an appropriate zero-curvature limit, we obtain the spherical functions on flat symmetric s...
In the setting of a metric measure space (X, d, µ) with an n-dimensional Radon measure µ, we give a ...
First published in the Bulletin of the American Mathematical Society in Vol.74, 1968, published by t...
This paper is concerned with defining Lipschitz spaces on Σn-1 the surface of the unit sphere in Rn....
In this paper Lipschitz spaces of distributions are defined and various inclusion relations are show...
In this paper the equivalence between the Campanato spaces and homogeneous Lipschitz spaces is shown...
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere S...
AbstractFunction spaces of Hardy–Sobolev–Besov type on symmetric spaces of noncompact type and unimo...
The main objective of this work is to develop a theory of Hardy spaces on the surface (SIGMA)(,N) of...
summary:We present explicit expressions of the Poisson kernels for geodesic balls in the higher dime...
We determine precise conditions for the boundedness of Bergman projections from Lebesgue classes ont...
AbstractWe use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions...
summary:If the Poisson integral of the unit disc is replaced by its square root, it is known that no...
AbstractWe continue a program to develop layer potential techniques for PDE on Lipschitz domains in ...
Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α...
By taking an appropriate zero-curvature limit, we obtain the spherical functions on flat symmetric s...
In the setting of a metric measure space (X, d, µ) with an n-dimensional Radon measure µ, we give a ...
First published in the Bulletin of the American Mathematical Society in Vol.74, 1968, published by t...