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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006