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1
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Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1

100%
Colzani L., Sjögren P.
Studia Mathematica
|
1999
|
tom 132
|
nr 2
101-124
EN
We study convolution operators bounded on the non-normable Lorentz spaces $L^{1,q}$ of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on $L^{1,q}$. In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals, we give a necessary and sufficient condition. This condition is, however, only sufficient in the general case.
2
Content available remote

Singular integrals on the complex affine group

100%
Gaudry G., Sjögren P.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
133-148
3
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Sharp estimates of the Jacobi heat kernel

100%
Nowak A., Sjögren P.
Studia Mathematica
|
2013
|
tom 218
|
nr 3
219-244
EN
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that the maximal operator of the multi-dimensional Jacobi heat semigroup satisfies a weak type (1,1) inequality. We also obtain sharp estimates of the Poisson-Jacobi kernel.
4
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On the boundary convergence of solutions to the Hermite-Schrödinger equation

100%
Sjögren P., Torrea J.
Colloquium Mathematicum
|
2010
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tom 118
|
nr 1
161-174
EN
In the half-space $ℝ^{d} × ℝ₊$, consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on $ℝ^{d}$. We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.
5
Content available remote

Hardy and Lipschitz spaces on subsets of $R^{n}$

60%
Jonsson A., Sjögren P., Wallin H.
Studia Mathematica
|
1984
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tom 80
|
nr 2
141-166
6
Content available remote

On the convergence of bilinear and quadratic forms in independent random variables

60%
Sjögren P.
Studia Mathematica
|
1981-1982
|
tom 71
|
nr 3
285-296
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