Abstract
We study the singular values of the commutator between multiplication by a function b(x) and singular integral operators acting on L2 (R). The relation between the smoothness of b(x) (measured using the Besov scale) and the decay of the singular values of the commutator (measured using the Schatten ideals) is well understood when the index, p, is greater than one. Here we offer results for the case p = 1. The simplest example, when the integral operator is the Hilbert transform, is atypical because of the algebraic simplicity of the kernel. Our methods are designed for more general kernels.
Partially supported by NSF grant DMS 8701271.
Partially supported by an NSF postdoctoral fellowship.
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© 1988 Birkhäuser Verlag Basel
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Rochberg, R., Semmes, S. (1988). End Point Results for Estimates of Singular Values of Singular Integral Operators. In: Gohberg, I., Helton, J.W., Rodman, L. (eds) Contributions to Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 35. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9284-1_9
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DOI: https://doi.org/10.1007/978-3-0348-9284-1_9
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