This paper presents a systematic study for abstract harmonic analysis on classical Banach spaces of covariant functions of characters of compact subgroups. Let G be a locally compact group and H be a compact subgroup of G. Suppose that \(\xi :H\rightarrow \mathbb {T}\) is a character, \(1\le p<\infty\) and \(L_\xi ^p(G,H)\) is the set of all covariant functions of \(\xi\) in \(L^p(G)\). It is shown that \(L^p_\xi (G,H)\) is isometrically isomorphic to a quotient space of \(L^p(G)\). It is also proven that \(L^q_\xi (G,H)\) is isometrically isomorphic to the dual space \(L^p_\xi (G,H)^*\), where q is the conjugate exponent of p. The paper is concluded by some results for the case that G is compact.

本文为紧致子群特征的协变函数的经典Banach空间提供了抽象谐波分析的系统研究。令G为局部紧致群，H为G的紧致子群。假设\（\ xi：H \ rightarrow \ mathbb {T} \）是一个字符，\（1 \ le p <\ infty \）和\（L_ \ xi ^ p（G，H）\）是集合的所有协变函数\（\ XI \）在\（L ^ p（G）\） 。证明\（L ^ p_ \ xi（G，H）\）等距同构于\（L ^ p（G）\）的商空间。也证明\（L ^ q_ \ xi（G，H）\）是对偶空间\（L ^ p_ \ xi（G，H）^ * \）的等距同构，其中q是p的共轭指数。对于G是紧实的情况，本文通过一些结果得出结论。