Related papers: Regularity of the centered fractional maximal func…

Let $\beta > 1$ be a real number and $x \in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\beta$-expansion of $x$…

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…

This paper investigates the regularity of stable radial solutions to semilinear elliptic equations arising in MEMS problems, modeled by the Dirichlet problem $-\Delta u=f(u)$ in the unit ball $B_1$, where the nonlinearity $f\in C^1([0,1))$…

In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions is extremely important. One of the reasons is that its error…

We study Hilbert functions of maximal Cohen-Macaulay(=CM) modules over CM local rings. We show that if $A$ is a hypersurface ring with dimension $d > 0$ then the Hilbert function of $M$ \wrt $\m$ is non-decreasing. If $A = Q/(f)$ for some…

We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions $M^{\a,\b}_t$ to be bounded on power weighted Lebesgue spaces. Moreover, we also obtain the corresponding…

By studying the spectral aspects of the fractional part function in a well-known separable Hilbert space, we show, among other things, a rational approximation of the Riemann zeta function and its derivatives valid on every vertical line in…

In this paper, we study $\beta$-dimensional sharp maximal operator defined as \begin{align*} \mathcal{M}^{\#} _\beta f(x) := \sup_{Q} \inf_{c \in \mathbb{R}} \chi_{Q}(x) \frac{1}{\ell(Q)^\beta} \int_Q |f-c| \; d \mathcal{H}^{\beta}_\infty,…

In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy-Littlewood maximal operator associated to certain families of doubling, radial decreasing…

The radial limits at a point ${\bf y}$ of the boundary of the domain $\Omega\subset {\bf R}^{2}$ of a bounded variational solution $f$ of Dirichlet or contact angle boundary value problems for a prescribed mean curvature equation are…

Let $f$ be a function on a bounded domain $\Omega \subseteq \mathbb{R}^n$ and $\delta$ be a positive function on $\Omega$ such that $B(x,\delta(x))\subseteq \Omega$. Let $\sigma(f)(x)$ be the average of $f$ over the ball $B(x,\delta(x))$.…

The paper shows that for any $G_\delta$ set $F$ of Lebesgue measure zero on the unit circle $T$ there exists a function $f \in H^{\infty}$ such that the radial limits of $f$ exist at each point of $T$ and vanish precisely on $F$. This…

Let $\rho_C$ be the regularity of the Hilbert function of a projective curve $C$ in $\mathbb P^n_K$ over an algebraically closed field $K$ and $\alpha_1,...,\alpha_{n-1}$ be minimal degrees for which there exists a complete intersection of…

Sharp $L^p$--$L^q$ estimates for the spherical maximal function over dilation sets of fractal dimensions, including the endpoint estimates, were recently proved by Anderson--Hughes--Roos--Seeger. More intricate $L^p$--$L^q$ estimates for…

In this article, we obtain some necessary and sufficient conditions for the boundedness of fractional Hausdorff operators $h_{\Phi,\beta}$ on weighted Lebesgue spaces $(0\leq\beta<1)$, which are fractional variants of Bandaliev-Safarova…

We study pointwise convergence of the fractional Schr\"odinger means along sequences $t_n$ which converge to zero. Our main result is that bounds on the maximal function $\sup_{n} |e^{it_n(-\Delta)^{\alpha/2}} f| $ can be deduced from those…

We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb{R}^2$, using circle tangency bounds when $\alpha \in (0,1]$ and a $\delta$-discretized slicing lemma for fractals when…

We show that generalized multiquadric radial basis functions (RBFs) on $\mathbb{R}^d$ have a mean dimension that is $1+O(1/d)$ as $d\to\infty$ with an explicit bound for the implied constant, under moment conditions on their inputs. Under…

In 1966, P. G\"unther proved the following result: Given a continuous function $f$ on a compact surface $M$ of constant curvature -1 and its periodic lift $\tilde{f}$ to the universal covering, the hyperbolic plane, then the averages of the…

This is a first version of a paper concerning abstract evolution equation with fractional time derivatives. Maximal regularity results in spaces of continuous and Hoelder continuous functions are described.