Let G be a locally compact group and \((\Phi , \Psi )\) be a complementary pair of N-functions. In this paper, the Fig\(\grave{\hbox {a}}\)–Talamanca–Herz algebras and the space of p-pseudomeasures on G are extended to Orlicz spaces. Indeed, the Banach algebra of \(\Phi \)-pseudomeasures \({\mathop {\mathrm{PM}}}_{\Phi }(G)\) and the Fig\(\grave{\hbox {a}}\)–Talamanca–Herz–Orlicz algebras \({\mathop {\mathrm{A}}}_{\Phi }(G)\) are defined. Then, it is shown that \({\mathop {\mathrm{A}}}_{\Phi }(G)^*={\mathop {\mathrm{PM}}}_{\Psi }(G)\). Furthermore, we characterize \(\mathop {\mathrm{Cv}}_{\Phi }(G)\), the space of \(\Phi \)-convoluters, in terms of right translation invariant operators on \(M^{\Phi }(G)\). Then when G is amenable, we show that \(\mathop {\mathrm{Cv}}_{\Phi }(G)\), is equal to \(\mathop {\mathrm{PM}}_{\Phi }(G)\), a generalization of the classical p-version. Finally, we study \(B_{\Phi }(G)\), the space of pointwise multipliers of \(\mathop {\mathrm{A}}_{\Phi }(G)\) when G is amenable.

中文翻译：

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图$$ \ grave {\ hbox {a}} $$ a`–Talamanca–Herz–Orlicz代数和Orlicz空间的卷积

令G为局部紧致群，\（（\ Phi，\ Psi）\）为N函数的互补对。在本文中，图\（\ grave {\ hbox {a}} \）– Talamanca–Herz代数和G上p-伪测度的空间被扩展到Orlicz空间。实际上，\（\ Phi \）-伪度量\（{\ mathop {\ mathrm {PM}}} _ {\ Phi}（G）\）的Banach代数和无花果\（\ grave {\ hbox {a} } \）– Talamanca–Herz–Orlicz代数\（{\ mathop {\ mathrm {A}}} _ {\ Phi}（G）\）被定义。然后，显示\（{\ mathop {\ mathrm {A}}} _ {\ Phi}（G）^ * = {\ mathop {\ mathrm {PM}}} __ {\ Psi}（G）\ ）。此外，我们根据\（M ^上的右平移不变算符来表征\（\ mathop {\ mathrm {Cv}} _ {\ Phi}（G）\），即\（\ Phi \）-卷积器的空间。{\ Phi}（G）\）。然后，当G合适时，我们证明\（\ mathop {\ mathrm {Cv}} _ {\ Phi}（G）\）等于\（\ mathop {\ mathrm {PM}} _ {\ Phi} （G）\），是经典p版本的推广。最后，我们研究\（B _ {\ Phi}（G）\），当G合适时，\（\ mathop {\ mathrm {A}} _ {\ Phi}（G）\）的点乘数的空间。