Related papers: On extremals for a Radon-like transform

In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces…

A parabolic integro differential operator operator L suitable to describe many phenomena in various physical fields,is considered. By means of equivalence between L and the third order equation which describe the evolution inside an…

For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to…

By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations.…

We prove that for a large class of functions $P$ and $Q$, there exists $d\in (0,1)$ such that the discrete bilinear Radon transform $$B^{\rm dis}_{P,Q}(f,g)(n)=\sum_{m\in\mathbb{Z}\setminus\{0\}} f(n-P(m))g(n-Q(m))\frac{1}{m}$$ is bounded…

We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\to L^r extension estimates for paraboloids. As a…

In this paper we study the regularity properties of certain maximal operators of convolution type at the endpoint $p=1$, when acting on radial data. In particular, for the heat flow maximal operator and the Poisson maximal operator, when…

We prove a sharp Lp estimate for a singular Radon transform according to a size condition of its kernel, which is useful for extrapolation.

We establish a supercritical Trudinger-Moser type inequality for the $k$-Hessian operator on the space of the $k$-admissible radially symmetric functions $\Phi^{k}_{0,\mathrm{rad}}(B)$, where $B$ is the unit ball in $\mathbb{R}^{N}$. We…

We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $\delta_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of…

Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…

In this paper, we establish Liouville-type theorems for parabolic differential inequalities with $(p,q)-$Laplacian operator on Riemannian manifolds. By a test function argument, we establish nonexistence results under suitable weighted…

We give a short, simple proof of maximal regularity for linear parabolic evolution equations on manifolds with cylindrical ends by making use of pseudodifferential parametrices and the concept of R-boundedness for the resolvent.

In this paper we establish the existence of extremal functions for weighted functionals with critical exponential growth in R^2, which arise from Henon-type equations. The proof is based on the notion of spherical symmetrization with…

In $L_2(\mathbb{R}^d)$, we consider a selfadjoint bounded operator ${\mathbb A}_\varepsilon$, $\varepsilon >0$, of the form $$ ({\mathbb A}_\varepsilon u) (\mathbf{x}) = \varepsilon^{-d-2} \int_{\mathbb{R}^d} a((\mathbf{x} - \mathbf{y} )/…

We study parabolic operators H = $\partial$t -- div $\lambda$,x A(x, t)$\nabla$ $\lambda$,x in the parabolic upper half space R n+2 + = {($\lambda$, x, t) : $\lambda$ > 0}. We assume that the coefficients are real, bounded, measurable,…

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with colinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing…

We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.

A boundary value problem related to a parabolic higher order operator with a small parameter is analized. When the small parameter tends to zero, the reduced operator is hyperbolic. When t tends to infinity a parabolic hyperbolic boundary…

We exhibit a smoothly bounded domain $\Omega$ with the property that for suitable $K\subset\partial \Omega$ and $z\in \Omega$ the "Sadullaev boundary relative extremal functions" satisfy the inequality…