New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
Copyright policy )New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications
AbstractIn this paper, we introduce and develop some new function spaces of BMO (bounded mean oscillation) type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type. The new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity, and they generalize the classical BMO space. We show that the John‐Nirenberg inequality holds on these spaces and they interpolate withLpspaces by the complex interpolation method. We then give applications onLp‐boundedness of singular integrals whose kernels do not satisfy the Hörmander condition. © 2005 Wiley Periodicals, Inc.
- Macquarie University Australia
- Zhongshan Hospital of Xiamen University China (People's Republic of)
- Sun Yat-sen University China (People's Republic of)
Singular and oscillatory integrals (Calderón-Zygmund, etc.), Banach spaces of continuous, differentiable or analytic functions, Interpolation between normed linear spaces, Abstract interpolation of topological vector spaces, Functions of bounded variation, generalizations, Inequalities for sums, series and integrals
Singular and oscillatory integrals (Calderón-Zygmund, etc.), Banach spaces of continuous, differentiable or analytic functions, Interpolation between normed linear spaces, Abstract interpolation of topological vector spaces, Functions of bounded variation, generalizations, Inequalities for sums, series and integrals
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