Related papers: The Fefferman-Stein type inequalities for strong a…

We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…

Motivated by the geometric reduction of Cauchy--Szeg\H{o} projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variable theory adapted to twisted multiparameter structures…

In this paper we investigate the boundedness of classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted…

The Coifman-Fefferman inequality implies quite easily that a Calderon-Zygmund operator $T$ acts boundedly in a Banach lattice $X$ on $\mathbb R^n$ if the Hardy-Littlewood maximal operator $M$ is bounded in both $X$ and $X'$. We discuss this…

In this article we study a special class of non-doubling metric measure spaces for which there is a significant difference between the incidence of weak and restricted weak type $(p,p)$ inequalities for the centered and non-centered…

For a Schwartz function $f$ on the plane and a non-zero $v\in\ZR^2$ define the Hilbert transform of $f$ in the direction $v$ to be $$ H_vf(x)=\text{p.v.}\int_\ZR f(x-vy) \frac{dy}y $$ Let $\zeta$ be a Schwartz function with frequency…

We prove two-weight norm inequalities for parabolic fractional maximal functions using parabolic Muckenhoupt weights. In particular, we prove a two-weight, weak-type estimate and Fefferman-Stein type inequalities for the centered parabolic…

We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ of Hardy-Littlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$…

We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…

Let $n\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\mathfrak M}{\alpha}$ of order $\alpha$, $0\le\alpha<n$, on the weighted Choquet-Lorentz space…

In this note, we establish a discrete method to characterize the limiting weak type behaviors of the centered Hardy-Littlewood maximal operator on the positive real axis through testing on Dirac deltas. As an application, we give some new…

We study generalized Poincar\'e inequalities. We prove that if a function satisfies a suitable inequality of Poincar\'e type, then the Hardy-Littlewood maximal function also obeys a meaningful estimate of similar form. As a by-product, we…

Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the…

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements.…

For $1<p<\infty$ and $M$ the centered Hardy-Littlewood maximal operator on $\mathbb{R}$, we consider whether there is some $\varepsilon=\varepsilon(p)>0$ such that $\|Mf\|_p\ge (1+\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\le…

Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…

In this article we investigate a special class of non-doubling metric measure spaces in order to describe the possible configurations of $P_{k,\rm s}^{\rm c}$, $P_{k,\rm s}$, $P_{k,\rm w}^{\rm c}$ and $P_{k,\rm w}$, the sets of all $p \in…

Given a space of homogeneous type $(X,\mu,d)$, we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L^\pp$. We prove that the variable Muckenhoupt condition…

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.

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,…