Nonmultipliers of the Sobolev spaces wk, 1 (Rn)
A Bonami, S Poornima - Journal of functional analysis, 1987 - Elsevier
Journal of functional analysis, 1987•Elsevier
While the class of multipliers of the Sobolev space W k, 1 (R n) is strictly larger than the
space of bounded measures for n> 1 [3], we show in this paper that it fails to contain certain
natural operators of the singular integral type (Theorem 1). To prove this, we consider the
analogous Sobolev space W̊ k, 1 of the homogeneous type and show that a nonconstant
homogeneous function of degree zero cannot be a Fourier multiplier of W̊ k, 1 (R
n)(Theorem 2). Some of the results of this paper were announced in [4].
space of bounded measures for n> 1 [3], we show in this paper that it fails to contain certain
natural operators of the singular integral type (Theorem 1). To prove this, we consider the
analogous Sobolev space W̊ k, 1 of the homogeneous type and show that a nonconstant
homogeneous function of degree zero cannot be a Fourier multiplier of W̊ k, 1 (R
n)(Theorem 2). Some of the results of this paper were announced in [4].
While the class of multipliers of the Sobolev space W k, 1 (R n) is strictly larger than the space of bounded measures for n> 1 [3], we show in this paper that it fails to contain certain natural operators of the singular integral type (Theorem 1). To prove this, we consider the analogous Sobolev space W̊ k, 1 of the homogeneous type and show that a nonconstant homogeneous function of degree zero cannot be a Fourier multiplier of W̊ k, 1 (R n)(Theorem 2). Some of the results of this paper were announced in [4].
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