Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1
Leonardo Colzani; Peter Sjögren
Studia Mathematica (1999)
- Volume: 132, Issue: 2, page 101-124
- ISSN: 0039-3223
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topColzani, Leonardo, and Sjögren, Peter. "Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1." Studia Mathematica 132.2 (1999): 101-124. <http://eudml.org/doc/216589>.
@article{Colzani1999,
abstract = {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.},
author = {Colzani, Leonardo, Sjögren, Peter},
journal = {Studia Mathematica},
keywords = {Lorentz space; convolution operator; real line; torus},
language = {eng},
number = {2},
pages = {101-124},
title = {Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1},
url = {http://eudml.org/doc/216589},
volume = {132},
year = {1999},
}
TY - JOUR
AU - Colzani, Leonardo
AU - Sjögren, Peter
TI - Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1
JO - Studia Mathematica
PY - 1999
VL - 132
IS - 2
SP - 101
EP - 124
AB - 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.
LA - eng
KW - Lorentz space; convolution operator; real line; torus
UR - http://eudml.org/doc/216589
ER -
References
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