Related papers: Fractional Hardy inequalities and capacity density

In this paper we prove a fractional version of a Caffarelli-Kohn-Nirenberg type interpolation inequality on hypersurfaces $M\subset\R^{n+1}$ which are boundaries of convex sets. The inequality carries a universal constant independent of $M$…

We give a short proof of a recently established Hardy-type inequality due to Keller, Pinchover, and Pogorzelski together with its optimality. Moreover, we identify the remainder term which makes it into an identity.

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.

We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…

We investigate the fractional Orlicz boundary Hardy-type inequality for bounded Lipschitz domains. Further, we establish fractional Orlicz boundary Hardy-type inequalities with logarithmic corrections for specific critical cases across…

In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem…

Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…

This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those…

In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

We present an inequality that classifies mixed multipartite systems of an arbitrary dimension with respect to separability and positivity of partial transpose properties. This inequality gives a way to experimentally classify the observed…

We consider fractional Hartree and cubic nonlinear Schr\"odinger equations on Euclidean space $\mathbb R^d$ and on torus $\mathbb T^d$. We establish norm inflation (a stronger phenomena than standard ill-posedness) at every initial data in…

We define and prove existence of fractional $P(\phi)_1$-processes as random processes generated by fractional Schr\"odinger semigroups with Kato-decomposable potentials. Also, we show that the measure of such a process is a Gibbs measure…

This note develops certain sharp inequalities relating the fractional Sobolev capacity of a set to its standard volume and fractional perimeter.

Transport experiments provide conflicting evidence on the possible existence of fractional order within integer quantum Hall systems. In fact integer edge states sometimes behave as monolithic objects with no inner structure, while other…

The sharpness of various Hardy-type inequalities is well-understood in the reversible Finsler setting; while infinite reversibility implies the failure of these functional inequalities, cf. Krist\'aly, Huang, and Zhao [Trans. Am. Math.…

We show that, when $sp>N$, the sharp Hardy constant $\mathfrak{h}_{s,p}$ of the punctured space $\mathbb R^N\setminus\{0\}$ in the Sobolev-Slobodecki\u{\i} space provides an optimal lower bound for the Hardy constant…

We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…

For doubling weights, we obtain a necessary and sufficient condition such that the one weighted inequality of the integral operator induced by Hardy kernels on the unit disk holds. This confirms a conjecture by Guo and Wang in such…

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy--Littlewood--Sobolev theorem in this context. In our main result, we investigate the dependence of…