Logarithmic summability of Fourier series.

Tkebuchava, G.

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We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces $C^{1} (G)$ and $W_{p}^{1} (G)$ . Further, we consider the Cauchy problem for this operator.

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Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

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We establish a Carleman type inequality for the subelliptic operator $ℒ = Δ_{z} + | x |^{2} \partial_{t}^{2}$ in $ℝ^{n + 1}$ , $n \geq 2$ , where $z \in ℝ^{n}$ , $t \in ℝ$ . As a consequence, we show that $- ℒ + V$ has the strong unique continuation property at points of the degeneracy manifold ${(0, t) \in ℝ^{n + 1} | t \in ℝ}$ if the potential $V$ is locally in certain $L^{p}$ spaces.

On $L_{1}$ convergence of certain cosine sums with twice quasi semi-convex coefficients.

Braha, N.L. (2010)

APPS. Applied Sciences

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