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The \( L^{p} \) -boundedness of pseudo-differential operators of different classes of symbols was investigated by Calder \(\acute{o}\) n and Vaillancourt [1], Fefferman [2], Illner [3], Cato [4], Nagase [5], Hwang and Lee [6], Wong [7] and studied various properties by exploiting the Fourier transform theory. Utilizing the Hankel transform theory, Pathak and Upadhyay [8] established the \( L_{\mu }^{p}\) -boundedness results and its various properties of the pseudo-differential operator with symbol class \( H^{0} \) . Using \( L_{\mu }^{p}\) -boundedness properties, the pseudo-differential operator \( h_{\mu ,a} \) is bounded linear operator from \(W_{\mu }^{m,p} \rightarrow W_{\mu }^{0, p} \) and \(W_{\mu }^{s,p} \rightarrow W_{\mu }^{s-m,p} \) respectively, where \(W_{\mu }^{s,p} \) is \(L_{\mu }^{p}(0,\infty )\) -Sobolev space of order s.

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\(L^{p}_{\alpha }(\mathbb {R}^{n+1}_{+})\) -Boundedness of Pseudo-Differential Operators Involving the Weinstein Transform

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  • 发表日期：

    2026年

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  • Santosh Kumar Upadhyay,
  • Mohd Sartaj

摘要

The \( L^{p} \) -boundedness of pseudo-differential operators of different classes of symbols was investigated by Calder \(\acute{o}\) n and Vaillancourt [1], Fefferman [2], Illner [3], Cato [4], Nagase [5], Hwang and Lee [6], Wong [7] and studied various properties by exploiting the Fourier transform theory. Utilizing the Hankel transform theory, Pathak and Upadhyay [8] established the \( L_{\mu }^{p}\) -boundedness results and its various properties of the pseudo-differential operator with symbol class \( H^{0} \) . Using \( L_{\mu }^{p}\) -boundedness properties, the pseudo-differential operator \( h_{\mu ,a} \) is bounded linear operator from \(W_{\mu }^{m,p} \rightarrow W_{\mu }^{0, p} \) and \(W_{\mu }^{s,p} \rightarrow W_{\mu }^{s-m,p} \) respectively, where \(W_{\mu }^{s,p} \) is \(L_{\mu }^{p}(0,\infty )\) -Sobolev space of order s.