ISSN:
1420-8989
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Banach algebras of certain bounded operators acting on the half-spaceL p (R + n+1 ,x 0 α ) (1〈p〈∞, −1〈α〈p−1) are defined which contain for example Wiener-Hopf operators, defined by multidimensional singular convolution integral operators, as well as certain singular integral operators with fixed singularities. Moreover the symbol may be a positive homogeneous function only piecewise continuous on the unit sphere. Actually these multidimensional singular integral operators may be not Calderón-Zygmund operators but are built up by those in lower dimensions. This paper is a continuation of a joint paper of the author together with R.V. Duduchava [10]. The purpose is to investigate invertibility or Fredholm properties of these operators, while the continuity is given by definition. This is done in [10] forp=2 and −1〈α〈1, and in the present paper forL p (R + n+1 ,x 0 α ) with 1〈p〈∞ and −1〈α〈p−1.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01195295
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