The Pointwise Convergence Along Curve Associated with Boussinesq Operator

In this paper, we study the almost everywhere pointwise convergence of the Boussinesq operator along curve γ(x, t) in ℝ. It is shown that \({\lim _{t \to 0}}{{\cal B}_t}f(\gamma (x,t)) = f(x)\) $${\lim }_{t\to 0}{ℬ}_{t}f(\gamma (x,t))=f(x)$$ almost everywhere for all f ∈ H^s(ℝ) provided that \(s \ge {1 \over 4}\) $$s\ge \frac{1}{4}$$ .