Abstract
In this paper, we establish an endpoint estimate for the commutator, [b, T], of a class of pseudodifferential operators T with symbols in Hörmander class . In particular, there exists a nontrivial subspace of such that, when b belongs to this subspace, the commutators [b, T] is bounded from into , which we extend the well‐known result of Calderón‐Zygmund operators.
Highlights
Remark that if the symbol a(x, ξ) satisfies some particular assumptions, pseudodifferential operator T in Lmρ,δ is a Calderon-Zygmund operator
BMO(Rn) such that, the commutators of pseudodifferential operators T is bounded on weighted Hardy space H1ω(Rn), where the operators T associated with the symbols in the Holmander class Smρ,δ(Rn) and ω ∈ Ap(Rn)
It is worthy to pointing out that in [21], Liang et al found a proper subspaces of BMO(Rn), such that, the commutators of Calderon-Zygmund operator is bounded on weighted
Summary
Remark that if the symbol a(x, ξ) satisfies some particular assumptions, pseudodifferential operator T in Lmρ,δ is a Calderon-Zygmund operator (see, [7]). BMO(Rn) such that, the commutators of pseudodifferential operators T is bounded on weighted Hardy space H1ω(Rn), where the operators T associated with the symbols in the Holmander class Smρ,δ(Rn) and ω ∈ Ap(Rn). Given an infinitely differentiable function f ∈ Rn with compact supports and symbol a(x, ξ) ∈ Smρ,δ(Rn), the pseudodifferential operator T is defined by Let b ∈ BMO(Rn) and T be a Calderon-Zygmund operator.
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