An 𝑛-Dimensional Pseudo-Differential Operator Involving the Hankel Transformation
R S Pathak Akhilesh Prasad Manish Kumar
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An 𝑛-dimensional pseudo-differential operator (p.d.o.) involving the 𝑛-dimensional Hankel transformation is defined. The symbol class $H^m$ is introduced. It is shown that p.d.o.'s associated with symbols belonging to this class are continuous linear mappings of the 𝑛-dimensional Zemanian space $H_\mu(I^n)$ into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain $L^1$-norm inequality.
R S Pathak1 Akhilesh Prasad2 Manish Kumar2
Volume 133, 2023
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