In this article we revisit the inequalities of Kato and Ponce concerning the L r norm of the
Bessel potential J s=(1− Δ) s/2 (or Riesz potential D s=(− Δ) s/2) of the product of two …

This authoritative text studies pseudodifferential and Fourier integral operators in the
framework of time-frequency analysis, providing an elementary approach, along with …

In this paper, we derive long time L p− L q decay estimates, in the full range 1≤ p≤ q≤∞,
for time-dependent multipliers in which an interplay between an oscillatory component and a …

In this paper, we discuss a role of the potential term on the $ L^ 2$ estimate of the solution
itself for wave equations with/without a damping term. In the case of free waves, it is known …

In this paper, we establish a weighted Kato–Ponce inequality for mm factors in the endpoint
case. Furthermore, we extend the validity of the Kato–Ponce inequality from the class of …

We consider the Cauchy problems in Rn for the plate equation with a weighted L1-initial
data. We derive new optimal estimates of the L2-norm of solutions for n ¼ 1, 2, 3, 4. In …

Abstract We extend the Kato-Ponce inequality to a product of m functions, proving an
estimate currently missing from the literature. This study is motivated by the fact that the 3 …

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn–
Hilliard–Oono equation in the whole space ℝ 3 with the nonlinearity of the sub-quintic …

In this paper, we study the critical exponent for the beam equation with nonlinear memory,
ie, u_ tt+ Δ^ 2u= F (t, u), where F= ∫ 0^ tf (ts) N (u)(s, x) ds,\quad N (u) ≈| u|^ p. For suitable f …

We study the nonlinear Klein–Gordon (NLKG) equation on a manifold M in the nonrelativistic
limit, namely as the speed of light c tends to infinity. In particular, we consider a higher-order …