The properties of a transformation $$f\mapsto {\tilde{f}}_h$$ by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that $$\left({\tilde{f}}_h\right)\widetilde{{}_k}={\tilde{f}}_{h+k}$$ for certain complex h and k, and that $$f\left(t\right)=\underset{h\to 0^{+}}{lim}{\tilde{f}}_h\left(t\right)$$ , where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous...

Si determina una formula di inversione di alcune trasformate di Laplace che intervengono nell’analisi formale di problemi al contorno relativi ad una classe di mezzi dissipativi. Le espressioni esplicite proposte definiscono funzioni analitiche a decrescenza rapida dotate di numerose proprietà di massimo, utili anche all’analisi di problemi unilaterali.

On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.

In this paper, we introduce certain multidimensional generalized Kober operators associated with the Gauss's hypergeometric function, which provide an elegant multivariate analogue of the operators introduced by Saxena and Kumbhat.

In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_{\alpha }^{+}$ from $L^p\left(v\right)$ into $L^p\left(w\right)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p:1\le p<\infty$ there exist non-trivial weights $w$ such that $I_{\alpha }^{+}$ is bounded from $L^p\left(w\right)$ into itself, even in the case $\alpha >1$.

Let $C{V}_p\left(F\right)$ be the left convolution operators on $L^p\left(G\right)$ with support included in F and $M_p\left(F\right)$ denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that $C{V}_p\left(F\right)$, $C{V}_p\left(F\right)/M_p\left(F\right)$ and $C{V}_p\left(F\right)/W$ are as big as they can be, namely have $l^{\infty }$ as a quotient, where the ergodic space W contains, and at times is very big relative to $M_p\left(F\right)$. Other subspaces of $C{V}_p\left(F\right)$ are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

Let S be an abelian *-semigroup. In this paper we prove some equivalent conditions for that every positive function is a moment function on S + S + S with a unique representation measure on the set of characters of S.