Let $\omega _{i}$ be weight functions on $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion $, (i=1,2,3,4). In this work, we define $CW_{\omega _{1},\omega _{2},\omega _{3},\omega _{4}}^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $ to be vector space of $\left( f,g\right) \in \left( L_{\omega _{1}}^{p}\times L_{\omega _{2}}^{q}\right) \left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $ such that the $\tau -$Wigner transforms $W_{\tau }\left( f,.\right) $ and $W_{\tau }\left( .,g\right) $ belong to $L_{\omega _{3}}^{r}\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2}\right) $ and $L_{\omega _{4}}^{s}\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2}\right) $ respectively for $1\leq p,q,r,s<\infty $, $\tau \in \left( 0,1\right) $. We endow this space with a sum norm and prove that $% CW_{\omega _{1},\omega _{2},\omega _{3},\omega _{4}}^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $ is a Banach space. We also show that $CW_{\omega _{1},\omega _{2},\omega _{3},\omega _{4}}^{p,q,r,s,\tau }\left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $ becomes an essential Banach module over $\left( L_{\omega _{1}}^{1}\times L_{\omega _{2}}^{1}\right) \left( %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion \right) $. We then consider approximate identities.

In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hypermodules. Moreover, we provide some relevant properties of the hypermodule in this topological hyperspace.

The wavelet transform is an useful mathematical tool. It is a mapping of a time signal to the time-scale joint representation. The wavelet transform is generated from a wavelet function by dilation and translation. This wavelet function satisfies an admissible condition so that the original signal can be reconstructed by the inverse wavelet transform. In this study, we firstly give some basic properties of the weighted variable exponent amalgam spaces. Then we investigate the convergence of the θ-means of f in these spaces under some conditions. Finally, using these results the convergence of the inverse continuous wavelet transform is considered in these spaces.

In this paper we first introduce multilinear fractional wavelet transform on ${\mathbb{R}}^n\times {\mathbb{R}}_{+}^n$ using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.