engleski

Distributions of anisotropic order and applications to H-distributions

We define distributions of anisotropic order on manifolds, and establish their immediate properties. The central result is the Schwartz kernel theorem for such distributions, allowing the representation of continuous operators from $C^l_c(X)$ to $(C^m_c(Y))′$ by kernels, which we prove to be distributions of order $l$ in $x$, but higher, although still finite, order in $y$. Our main motivation for introducing these distributions is to obtain the new result that H-distributions (Antonić and Mitrović), a recently introduced generalization of H- measures are, in fact, distributions of order 0 (i.e. Radon measures) in $x\in\mathbb{; ; ; ; ; R}; ; ; ; ; ^d$, and of finite order in $\xi\in S^{; ; ; ; ; d−1}; ; ; ; ; $. This allows us to obtain some more precise results on H-distributions, hopefully allowing for further applications to partial differential equations.

Fourier multiplier ; H-measure ; H-distribution ; distribution of finite order ; Schwartz kernel theorem

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