q-Variation and Commutators for Fourier Multipliers
نویسنده
چکیده
If Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded q-variation on dyadic coronas, we prove that the commutator [T, Tμ] = TTμ−TμT is bounded on the Besov space B p (R ), if T is any bounded linear operator on a couple of Besov spaces Bj ,rj p (R) (j = 0, 1, and 0 < σ1 < σ < σ0).
منابع مشابه
Commutators for Fourier multipliers on Besov Spaces
The mapping properties of commutators [T,M ] = TM −MT , for operators between function spaces, and their various generalizations play an important role in harmonic analysis, PDE, interpolation theory and other related areas. A typical situation arises when M = Mb is the pointwise multiplication by a function b and T is a Calderón–Zygmund operator on R. Then well– known results of A.P. Calderón ...
متن کاملMultipliers of pg-Bessel sequences in Banach spaces
In this paper, we introduce $(p,q)g-$Bessel multipliers in Banach spaces and we show that under some conditions a $(p,q)g-$Bessel multiplier is invertible. Also, we show the continuous dependency of $(p,q)g-$Bessel multipliers on their parameters.
متن کاملHyperbolic L Multipliers are Translations
The associated evolution operators which map u(0, ·) to u(t, ·) is the family of Fourier multipliers e, e := F e F . (2) Our main result shows that boundedness in L for p 6= 2 is very rare. The evolution operator is L bounded if and only if it consists of simple translations. If the multiplier (2) is an L multiplier then it is an L multiplier for the dual index, p+q = 1. By interpolation it is ...
متن کاملDUHAMEL SOLUTIONS OF NON-HOMOGENEOUS q-ANALOGUE WAVE EQUATIONS
q-analogue non-homogeneous wave equations are solved by a Duhamel solution strategy using constructions with q-analogue Fourier multipliers to compensate for the dependence of the analogue differential Leibnitz rule on the parity of the functions involved.
متن کاملNew Thoughts on the Vector-valued Mihlin–hörmander Multiplier Theorem
Abstract. Let X be a UMD space with type t and cotype q, and let Tm be a Fourier multiplier operator with a scalar-valued symbol m. If |∂m(ξ)| . |ξ|−|α| for all |α| ≤ ⌊n/max(t, q′)⌋ + 1, then Tm is bounded on L(R;X) for all p ∈ (1,∞). For scalar-valued multipliers, this improves the theorem of Girardi and Weis (J. Funct. Anal., 2003) who required similar assumptions for derivatives up to the or...
متن کامل