A note on operator-valued Fourier multipliers on Besov spaces

作者：Bu SQ^*; Kim JM

来源：Mathematische Nachrichten, 2005, 278(14): 1659-1664.

DOI：10.1002/mana.200310330

• operator-valued Fourier multiplier
• Besov spaces
• UMD spaces
• Hilbert spaces

Let X be a Banach space. We show that each m : R backslash {0} -> L(Chi) satisfying the Mikhlin condition sup(x not equal 0) (parallel to m(x)parallel to + parallel to xm'(x)parallel to) < infinity defines aFourier multiplieron B(p)(s),q(R; X) if and only if 1 < p < infinity and X is isomorphic to a Hilbert space; each bounded measurable function m : R -> L(X) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B(p)(s),q (R; X) if and only if 1 < p < infinity P and X is a UMD space.

• 出版日期2005
• 单位清华大学