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Multilinear commutators for fractional integrals in non-homogeneous spaces.

Guoen Hu, Yan Meng, Dachung Yang (2004)

Publicacions Matemàtiques

Under the assumption that m is a non-doubling measure on Rd, the authors obtain the (Lp,Lq)-boundedness and the weak type endpoint estimate for the multilinear commutators generated by fractional integrals with RBMO (m) functions of Tolsa or with Osc exp Lr(m) functions for r greater than or equal to 1, where Osc exp Lr(m) is a space of Orlicz type satisfying that Osc exp Lr(m)=RBMO(m) if r=1 and Osc exp Lr(m) is a subset of RBMO(m) if r>1.

Multiplicative maps that are close to an automorphism on algebras of linear transformations

L. W. Marcoux, H. Radjavi, A. R. Sourour (2013)

Studia Mathematica

Let be a complex, separable Hilbert space of finite or infinite dimension, and let ℬ() be the algebra of all bounded operators on . It is shown that if φ: ℬ() → ℬ() is a multiplicative map(not assumed linear) and if φ is sufficiently close to a linear automorphism of ℬ() in some uniform sense, then it is actually an automorphism; as such, there is an invertible operator S in ℬ() such that φ ( A ) = S - 1 A S for all A in ℬ(). When is finite-dimensional, similar results are obtained with the mere assumption that there...

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