Related papers: Multi-parameter fractional integration on Heisenbe…
We discuss the asymptotic behaviour for the best constant in L^p-L^q estimates for trigonometric polinomials and for an integral operator which is related to the solution of inhomogeneous Schrodinger equations. This gives us an opportunity…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
In this article, we introduce the fractional medians, give an expression of the set of all fractional medians in terms of non-increasing rearrangements and then investigate mapping properties of the fractional maximal operators defined by…
Consider the surface measure $\mu$ on a sphere in a nonvertical hyperplane on the Heisenberg group $\mathbb{H}^n$, $n\ge 2$, and the convolution $f*\mu$. Form the associated maximal function $Mf=\sup_{t>0}|f*\mu_t|$ generated by the…
In this article,we present exactly when two classes of multiparameter Forelli-Rudin type integral operators are bounded from one weighted mixed-norm Lebesgue space $L^{\vec{p}}$ to another space $L^{\vec{q}}$ over the Siegel upper…
We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition $s>d\left|1/p-1/2\right|$, where $d$ is the topological dimension of the underlying group. Our approach relies…
In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of fractional maximal singular integral operators $T_{\Omega,\alpha}^{\#}$ with homogeneous convolution kernel…
In this paper we construct conformally invariant systems of first order and second order differential operators associated to a homogeneous line bundle $\Cal{L}_{s} \to G_0/Q_0$ with $Q_0$ a maximal parabolic subgroup of quasi-Heisenberg…
Various notions of dissipativity type for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case $L^p$-dissipativity. Most of the results are due to the authors.
We determine exactly when two classes of integral operators are bounded on weighted $L^p$ spaces over the Siegel upper half-space.
We establish partial semigroup property of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order…
We extend our previous definition of K-theoretic invariants for operator systems based on hermitian forms to higher K-theoretical invariants. We realize the need for a positive parameter $\delta$ as a measure for the spectral gap of the…
We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. These results allow us to obtain the boundedness of Dunkl-type fractional integral and fractional maximal operators in the Dunkl-Fofana spaces.
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
In this work we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional…
We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish H\"ormander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible…
We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schr\"odinger equation. In this work, we establish the existence…