Related papers: Weighted norm inequalities for k-plane transforms
We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing…
We describe the range of of weighted Cauchy transform and its $k$-Bergman projection when action on weighted true poly-Bargmann spaces constituting an orthogonal Hilbertian decomposition of the Hilbert space of Gaussian functions on the…
Let $v,~\omega_1, ~\omega_2$ be weights and $1<p_1, ~p_2<\infty.$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ in martingale…
We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best…
This paper explores refinements of some operator norm inequalities through the generalized spherical Aluthge transform and the spherical Heinz transform. We introduce the spherical Schatten $p$-norm for operator tuples and establish several…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
We consider weighted norm inequalities for the Riesz potentials $I_\alpha$, also referred to as fractional integral operators. First we prove mixed $A_p$-$A_\infty$ type estimates in the spirit of [13, 15, 17]. Then we prove strong and weak…
The inverse problem for the Euler-Poisson-Darboux equation deals with reconstruction of the Cauchy data for this equation from incomplete information about its solution. In the present article, this problem is studied in connection with the…
We prove weighted strong $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators. For the first family of operators the weights used can be either Sawyer's one-sided $A^+_p$ weights or Muckenhoupt's…
The $k$-plane transform is a bounded operator from $\lp$ to $L^q$ of the Grassmann manifold of all affine $k$-planes in $\R^n$ for certain exponents depending on $k$ and $n$. In the endpoint case $q=n+1$, we identify all extremizers of the…
We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…
We give a classification between weighted norm inequalities of strong fractional integral operators, and their associated multi-parameter Muckenhoupt characteristics, bu considering the weights to be power functions. As a result, we extend…
We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
In this paper one-weight inequalities with general weights for Riemann-Liouville transform and $ n-$ dimensional fractional integral operator in variable exponent Lebesgue spaces defined on $\mathbb{R}^{n}$ are investigated. In particular,…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
In this paper, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert…
Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…
We consider L^p two weight inequalities for maximal truncations of dyadic Calderon-Zygmund operators. In the case of one weight being doubling, a characterization is given, and for the general case, sufficient conditions are given,…