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We study the continuity of pseudo-differential operators on
Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces
B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy
j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.
We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
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