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The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.
We establish the Heisenberg–Pauli–Weyl uncertainty inequalities for Fourier transform and the continuous wavelet transform on the Heisenberg group.
We establish the Calderon reproducing formula for functions in on the Heisenberg group . Also, we develop this formula in with .
Let F2n,2 be the free nilpotent Lie group of step two on 2n generators, and let P denote the affine automorphism group of F2n,2. In this article the theory of continuous wavelet transform on F2n,2… (More)
This article presents the Heisenberg–Pauli–Weyl uncertainty inequality for the Radon transform on the Heisenberg group, which indicates that the Radon transform and the Fourier transform of a nonzero… (More)
In this article, two types of Hardy’s inequalities for the twisted convolution with Laguerre functions are studied. The proofs are mainly based on an estimate for the Heisenberg left-invariant… (More)
In this article, we establish new oscillation criteria for the secondorder Emden-Fowler neutral delay differential equation “ r(t)|z′(t)|α−1z′(t) ”′ + q(t)|x(σ(t))|β−1x ` σ(t) ́ = 0, where z(t) =… (More)
AbstractIn this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral type … (More)
SummaryWe apply the squeeze theorem, instead of L′Hospital′s rule, to evaluate limits in indeterminate form of exponential type. We do not require differentiability, instead needing the boundedness...
This article presents two types of Hardy’s inequalities for the Heisenberg group. The proofs are mainly based on estimates of the Fourier transform for atomic functions deduced by the horizontal… (More)