2025/03/13 by Tuan, Trinh · 1 citation
#42A38 #44A20 #44A35 #45A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2503.10243
Using Kakichev's classical concept and extending Yakubovich-Britvina's approach (Results. Math. 55(1-2):175-197, 2009) and (Integral Transforms Spec. Funct. 21(4):259--276, 2010) for setting up Kontorovich-Lebedev convolution operators, this paper proposes a new polyconvolution structure associated with the KL-transform and Fourier integrals. Our main contributions include demonstrating a one-dimensional Watson-type transform, providing necessary and sufficient conditions for this transform to serve as unitary on L2(ℝ+), and inferring its inverse operator in symmetric form. The existence of this structure over specific function spaces and its connection with previously known convolutions are pointed out. Establish the Plancherel-type theorem, prove the convergence in the mean-square sense in L2(ℝ+), and prove the boundedness of dual spaces via Riesz-Thorin's theorem. Derives new weighted Lp-norm inequalities and boundedness in a three-parametric family of Lebesgue spaces. These theoretical findings are applied to solve specific classes of the Toeplitz-Hankel equation, providing a priori estimations based on the established conditions for L1 solvability.