We introduce new anisotropic wavelet-type transforms generated by two components: a wavelet measure (or a wavelet function) and a kernel function that naturally generalizes the Gauss and Poisson kernels. The analogues of Calderon’s reproducing formula are established in the framework of the \(L_{p}(\mathbb {R}^{n+1})\)-theory. These wavelet-type transforms have close connection with a significant generalization of the classical parabolic-Riesz and parabolic-Bessel potentials and can be used to find explicit inversion formulas for the generalized parabolic-type potentials.

中文翻译：

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类似于抛物线的小波变换和相关的再现公式

我们介绍了由两个分量生成的新的各向异性小波类型变换：小波测度（或小波函数）和自然泛化高斯和泊松核的核函数。Calderon复制公式的类似物是在\（L_ {p}（\ mathbb {R} ^ {n + 1}）\）理论的框架内建立的。这些小波类型的变换与经典抛物线-Riesz势和抛物线-Bessel势的显着推广有着密切的联系，可以用来为广义的抛物线型势找到明确的反演公式。