Functions of a second order elliptic operator in rearrangement invariant spaces. (English) Zbl 0837.46022

Summary: The functional calculus of positive operators is applied to second-order elliptic operators \(P\). For any absolutely concave \(\varphi(t)\), the corresponding operators \(\varphi(P^{- 1})\) are represented as integral operators, their kernels are estimated, and these estimates are used for studying \(\varphi(P^{- 1})\) in Lorentz, Marcinkiewicz and Orlicz spaces. Most of the results obtained are sharp.


46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47F05 General theory of partial differential operators
47B38 Linear operators on function spaces (general)
35J99 Elliptic equations and elliptic systems
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