Related papers: A sharp boundedness result concerning some maximal…

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue…

The main aim of this paper is to prove that when $0<p<1/2$ the maximal operator $\overset{\sim }{\sigma }_{p}^{\ast }f:=\underset{n\in \mathbb{N}}{% \sup }\frac{\left\vert \sigma_{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded…

The main aim of this paper is to prove that the maximal operator $\overset{% \sim }{\sigma }^{*}f:=\underset{n\in P}{\sup }\frac{\left| \sigma_{n}f\right| }{\log ^{2}\left( n+1\right) }$ is bounded from the Hardy space $H_{1/2}$ to the…

In this paper we derive the maximal subspace of natural numbers $\left\{n_{k}:k\geq 0\right\}$, such that the restricted maximal operator, defined by $\sup_{k\in \mathbb{N}}\left\vert \sigma_{n_{k}}F \right\vert$ on this subspace of Fej\'er…

In this paper we characterize subsequences of Fej\'er means with respect to Vilenkin systems, which are bounded from the Hardy space $H_{p}$ to the Lebesgue space $L_{p},$ for all $0<p<1/2.$ The result is in a sense sharp.

In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert \sigma _{k}F\right\vert/A^2_k\right)$ of Fej\'er means of Walsh-Fourier series and prove that the it is bounded from the…

The main aim of this paper is to prove that the maximal operator $\sigma_{p}^{\kappa ,\ast }f:=\sup_{n\in \mathbf{P}}\left\vert \sigma_{n}^{\kappa }f\right\vert /\left( n+1\right) ^{1/p-2}$ is bounded from the Hardy space $% H_{p}$ to the…

As main result we prove that Fej\'er means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space $\ H_{p}$ to the Hardy martingale space $H_{p}$ for $ 0<p\leq 1/2.$

Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \geq 0$ for which boundedness from the Sobolev space $H^s(\mathbb{R})$ into…

We study the boundedness problem for maximal operators $\M$ associated to smooth hypersurfaces $S$ in 3-dimensional Euclidean space. For $p>2,$ we prove that if no affine tangent plane to $S$ passes through the origin and $S$ is analytic,…

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds…

We provide characterizations for boundedness of multilinear Fourier operators on Hardy-Lebesgue spaces with symbols locally in Sobolev spaces. Let $H^q(\mathbb R^n)$ denote the Hardy space when $0<q\le 1$ and the Lebesgue space $L^q(\mathbb…

In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh-Fourier series. We prove that for some "optimal" weights these new operators indeed are bounded from the martingale Hardy space $H_{p}$ to the…

We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p\leq 1.$ We also prove that the sequence in…

As main result we prove that Fej\'er means of Walsh-Fourier series are uniformly bounded operators from $\ H_{p}$ to $H_{p}$ $\left( 0<p\leq 1/2\right) .

The main aim of this paper is to investigate weighted maximal operators of partial sums of Vilenkin-Fourier series. We also use our results to prove approximation and strong convergence theorems on the martingale Hardy spaces $H_{p},$ when…

We find optimal conditions on $m$-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces $H^{p_j}$, $0<p_j\le 1$, to Lebesgue spaces $L^p$. The conditions we obtain are necessary and sufficient for…

We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the…

The properties of the maximal operator of the $(C,\alpha)$-means ($\alpha=(\alpha_1,\ldots,\alpha_d)$) of the multi-dimensional Walsh-Kaczmarz-Fourier series are discussed, where the set of indices is inside a cone-like set. We prove that…

We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its dual space $L^{p'(\cdot)}$, where…