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 Vietnam Journal of Mathematics 38:4 (2010) 425-433 Behavior of the Sequence of Norms of Primitives of a Function in Lorentz Space Ha Huy Bang and Bui Viet Huong Abstract.  Let $f\in \Psi(\mathbb R)$ and $I^nf\in N_\Psi(\mathbb R)$, for all $n = 1, 2, ...$. Then $\mathop {\lim }\limits_{n \to \infty } ||I^n f||_{N_\Psi ()}^{1/n} = \sigma ^{ - 1},$ where $\sigma := \inf\{|\xi|: \xi \in \supp f\}, ||.||_N_\Psi(\mathbb R)$ is the norm in the Lorentz space $N_\Psi (\mathbb R)$, and for $g\in S'(\mathbb R)$, the tempered generalized function $Ig$ is a primitive of $g$ if $D(Ig) = g$, that is $\-, \forall \varphi \in S(\mathbb R)$ and $S(\mathbb R)$ is the Schwartz space of rapidly decreasing functions. In other words, in this paper we characterize behavior of the sequence of \$N_\Psi(\mathbb R) - norms of primitives of a function by its spectrum (the support of its Fourier transform). 2000 Mathematics Subject Classification: 46E30. Keywords: Lorentz spaces, primitives of generalized functions.

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