标题： 不变加权代数 $L_p^w(G)$ 显示英文标题

标题： Invariant weighted algebras $L_p^w(G)$

摘要： 本文讨论局部紧致群G上的加权空间$L_p^w(G)$。 如果w是G上的正可测函数，那么我们定义空间$L_p^w(G)$，$p\ge1$，作为$L_p^w(G)=\{f:fw\in L_p(G)\}$。 我们考虑这样的权函数，使得这些加权空间在通常的卷积下成为代数。 证明了对于p>1，任何sigma-compact群上都存在这样的权函数。 我们还证明了一个在特殊情况下早已知道的准则：$L_1^w(G)$是一个代数当且仅当w是次乘的。 证明了不变代数$L_p^w(G)$，$p>1$具有标准形式的近似单位，但对于非不变代数这可能不成立。 显示英文摘要

摘要： The paper deals with weighted spaces $L_p^w(G)$ on a locally compact group G. If w is a positive measurable function on G then we define the space $L_p^w(G)$, $p\ge1$, as $L_p^w(G)=\{f:fw\in L_p(G)\}$. We consider weights such that these weighted spaces are algebras with respect to usual convolution. It is shown that for p>1 such weights exists on any sigma-compact group. We prove also a criterion known earlier in special cases: $L_1^w(G)$ is an algebra if and only if w is submultiplicative. It is proved that invariant algebras $L_p^w(G)$, $p>1$, have approximate units of standard form, but this may not be true for a non-invariant algebra.