J. Rozendaal

activity

20122026

most citedOptimal rates of decay for operator semigroups on Hilbert spaces

81 citations · 237 across the 26 of their papers we have counts for

collaborators

28 papers

math.AP2026

Local smoothing for rough wave equations

Jan Rozendaal, Robert Schippa

We prove local smoothing estimates for wave equations with $C^{r}$ coefficients, relying on bilinear restriction estimates associated with rough wave propagation. In two and three…

math.AP2025

Propagation of singularities for equations with $C^{r}$ coefficients for $r > 1$

Jan Rozendaal

We observe that, for $r > 1$ , $s$ in an $r$ -dependent interval, $p$ a homogeneous pseudodifferential symbol of order $m$ having $C^{r}$ regularity in space, and $u\in H^{s+m-r}(\math…

math.AP2025

The Hardy spaces $H_{F I O}^{p} (R^{n})$ for Fourier integral operators for $p < 1$

Naijia Liu, Jan Rozendaal, Liang Song

We introduce the Hardy spaces $H_{F I O}^{p} (R^{n})$ for Fourier integral operators for $0 < p < 1$ , thereby extending earlier constructions for $1 \leq p \leq \infty$ .…

math.AP2025

$H^{1}$ and $bmo$ regularity for wave equations with rough coefficients

Naijia Liu, Jan Rozendaal, Liang Song

We consider second-order hyperbolic equations with rough time-independent coefficients. Our main result is that such equations are well posed on the Hardy spaces $\mathcal{H}^{s,1}…

math.FA2024★ 1 cited

Improved polynomial decay for unbounded semigroups

Chenxi Deng, Jan Rozendaal, Mark Veraar

We obtain polynomial decay rates for $C_{0}$ -semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the…

math.CA2024

Spherical maximal functions and Hardy spaces for Fourier integral operators

Abhishek Ghosh, Naijia Liu, Jan Rozendaal +1

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p} (R^{n})$ , $n \geq 2$ , where the radii of the spheres are res…

math.AP2023

Function spaces for decoupling

Andrew Hassell, Pierre Portal, Jan Rozendaal +1

We introduce new function spaces $L_{W, s}^{q, p} (R^{n})$ that yield a natural reformulation of the $ℓ^{q} L^{p}$ decoupling inequalities for the sphere and the…

math.AP2022★ 1 cited

Local smoothing and Hardy spaces for Fourier integral operators on manifolds

Naijia Liu, Jan Rozendaal, Liang Song +1

We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates fo…

math.FA2022★ 9 cited

Operator-valued $(L^{p}, L^{q})$ Fourier multipliers and stability theory for evolution equations

Jan Rozendaal

We give an overview of some recent results on operator-valued $(L^{p}, L^{q})$ Fourier multipliers and stability theory for evolution equations. The aim is to provide a relatively n…

math.AP2022★ 3 cited

Nonlinear wave equations with slowly decaying initial data

Jan Rozendaal, Robert Schippa

New local smoothing estimates in Besov spaces adapted to the half-wave group are proved via $ℓ^{2}$ -decoupling. We apply these estimates to obtain new well-posedness results for t…

math.AP2021★ 7 cited

Local smoothing and Hardy spaces for Fourier integral operators

Jan Rozendaal

We show that the Hardy spaces for Fourier integral operators form natural spaces of initial data when applying $ℓ^{p}$ -decoupling inequalities to local smoothing for the wave eq…

math.AP2021★ 5 cited

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II

Jan Rozendaal

We obtain improved bounds for pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a (x, η)$ are elements of $C^{r}_{*}S^{m}_{…

math.AP2020★ 1 cited

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators

Jan Rozendaal

We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a (x, η)$ are elements of $C^{r}_{*}S^{m}_…

math.AP2020★ 3 cited

$L^{p}$ and $H_{F I O}^{p}$ regularity for wave equations with rough coefficients

Andrew Hassell, Jan Rozendaal

We consider wave equations with time-independent coefficients that have $C^{1, 1}$ regularity in space. We show that, for nontrivial ranges of $p$ and $s$ , the standard inhomogeneou…

math.AP2019★ 4 cited

Characterizations of the Hardy space $H_{F I O}^{1} (R^{n})$ for Fourier integral operators

Zhijie Fan, Naijia Liu, Jan Rozendaal +1

The Hardy spaces for Fourier integral operators $H_{F I O}^{p} (R^{n})$ , for $1 \leq p \leq \infty$ , were introduced by Smith in [Smith,1998] and Hassell et al. in [H…

math.AP2019★ 8 cited

Characterizations of Hardy spaces for Fourier integral operators

Jan Rozendaal

We prove several characterizations of the Hardy spaces for Fourier integral operators $H_{F I O}^{p} (R^{n})$ , for $1 < p < \infty$ . First we characterize $\mathcal{H}^…

math.AP2018★ 18 cited

Off-singularity bounds and Hardy spaces for Fourier integral operators

Andrew Hassell, Pierre Portal, Jan Rozendaal

We define a scale of Hardy spaces $H_{F I O}^{p} (R^{n})$ , $p \in [1, \infty]$ , that are invariant under suitable Fourier integral operators of order zero. This builds…

math.FA2017★ 15 cited

Sharp growth rates for semigroups using resolvent bounds

Jan Rozendaal, Mark Veraar

We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if…

math.FA2017★ 14 cited

Stability theory for semigroups using $(L^{p}, L^{q})$ Fourier multipliers

Jan Rozendaal, Mark Veraar

We study polynomial and exponential stability for $C_{0}$ -semigroups using the recently developed theory of operator-valued $(L^{p}, L^{q})$ Fourier multipliers. We characterize pol…

math.FA2017★ 81 cited

Optimal rates of decay for operator semigroups on Hilbert spaces

Jan Rozendaal, David Seifert, Reinhard Stahn

We investigate rates of decay for $C_{0}$ -semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains th…

math.FA2016★ 11 cited

Fourier multiplier theorems on Besov spaces under type and cotype conditions

Jan Rozendaal, Mark Veraar

In this paper we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents $p$ and $q$ , which depend on the type $p$ and cotyp…

math.FA2016★ 16 cited

Fourier multiplier theorems involving type and cotype

Jan Rozendaal, Mark Veraar

In this paper we develop the theory of Fourier multiplier operators $T_{m} : L^{p} (R^{d}; X) \to L^{q} (R^{d}; Y)$ , for Banach spaces $X$ and $Y$ , $1\leq p\leq q\leq \i…

math.FA2015★ 5 cited

Functional calculus for $C_{0}$ -groups using (co)type

Jan Rozendaal

We study the functional calculus properties of generators of $C_{0}$ -groups under type and cotype assumptions on the underlying Banach space. In particular, we show the following.…

math.RT2015★ 8 cited

Disintegration of positive isometric group representations on $L^{p}$ -spaces

Marcel de Jeu, Jan Rozendaal

Let $G$ be a Polish locally compact group acting on a Polish space $X$ with a $G$ -invariant probability measure $μ$ . We factorize the integral with respect to $μ$ in terms of the i…

Local smoothing for rough wave equations

Propagation of singularities for equations with Cr coefficients for r>1

The Hardy spaces HFIOp​(Rn) for Fourier integral operators for p<1

H1 and bmo regularity for wave equations with rough coefficients

Improved polynomial decay for unbounded semigroups

Spherical maximal functions and Hardy spaces for Fourier integral operators

Function spaces for decoupling

Local smoothing and Hardy spaces for Fourier integral operators on manifolds

Operator-valued (Lp,Lq) Fourier multipliers and stability theory for evolution equations

Nonlinear wave equations with slowly decaying initial data

Local smoothing and Hardy spaces for Fourier integral operators

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II

Rough pseudodifferential operators on Hardy spaces for Fourier integral operators

Lp and HFIOp​ regularity for wave equations with rough coefficients

Characterizations of the Hardy space HFIO1​(Rn) for Fourier integral operators

Characterizations of Hardy spaces for Fourier integral operators

Off-singularity bounds and Hardy spaces for Fourier integral operators

Sharp growth rates for semigroups using resolvent bounds

Stability theory for semigroups using (Lp,Lq) Fourier multipliers

Optimal rates of decay for operator semigroups on Hilbert spaces

Fourier multiplier theorems on Besov spaces under type and cotype conditions

Fourier multiplier theorems involving type and cotype

Functional calculus for C0​-groups using (co)type

Disintegration of positive isometric group representations on Lp-spaces

Propagation of singularities for equations with $C^{r}$ coefficients for $r > 1$

The Hardy spaces $H_{F I O}^{p} (R^{n})$ for Fourier integral operators for $p < 1$

$H^{1}$ and $bmo$ regularity for wave equations with rough coefficients

Operator-valued $(L^{p}, L^{q})$ Fourier multipliers and stability theory for evolution equations

$L^{p}$ and $H_{F I O}^{p}$ regularity for wave equations with rough coefficients

Characterizations of the Hardy space $H_{F I O}^{1} (R^{n})$ for Fourier integral operators

Stability theory for semigroups using $(L^{p}, L^{q})$ Fourier multipliers

Functional calculus for $C_{0}$ -groups using (co)type

Disintegration of positive isometric group representations on $L^{p}$ -spaces