Related papers: Dyadic John-Nirenberg space
We study properties of $\mathcal{A}$-harmonic and $\mathcal{A}$-superharmonic functions involving an operator having generalized Orlicz-growth embracing besides Orlicz case also natural ranges of variable exponent and double-phase cases. In…
We prove a noncommutative version of the John-Nirenberg theorem for nontracial filtrations of von Neumann algebras. As an application, we obtain an analogue of the classical large deviation inequality for elements of the associated $BMO$…
We completely describe the boundedness of the Volterra type operator $J_ g$ between Hardy spaces in the unit ball of $\Cn$. The proof of the one dimensional case used tools, such as the strong factorization for Hardy spaces, that are not…
If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a…
The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…
We investigate the magnitude relation of the non-centered Hardy-Littlewood maximal operators and centered one. By using a discretization technique, we prove two facts: the first one is that the space is ultrametric if and only if the two…
The general Weyl -- Wigner formalism in finite dimensional phase spaces is investigated. Then this formalism is specified to the case of symmetric ordering of operators in an odd -- dimensional Hilbert space. A respective Wigner function on…
We obtain $L^p-$estimates for the full and lacunary maximal functions associated to the twisted bilinear spherical averages given by \[\mathfrak{A}_t(f_1,f_2)(x,y)=\int_{\mathbb S^{2d-1}}f_1(x+tz_1,y)f_2(x,y+tz_2)\;d\sigma(z_1,z_2),\;t>0,\]…
In this paper we find functions over bounded domains in the 2-dimensional Euclidean space, whose graphs (in the Heisenberg space) has constant mean curvature different from zero and taking on (possibly) infinite boundary values over the…
In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
We precisely compute the Bellman function of two variables of the dyadic maximal operator in relation to Kolmogorov inequality. In this way we give an alternative proof of the results in [5].Additionally, we characterize the sequences of…
We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us…
Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…
In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on certain Riemannian manifolds with bounded geometry. Our results complement those of various authors. We show that, under…
We defined several functionals on the set of all triangulations of the finite system of points in d-space achieving global minimum on the Delaunay triangulation (DT). We consider a so called "parabolic" functional and prove it attains its…
Consider a multiply-connected domain $\Sigma$ in the sphere bounded by $n$ non-intersecting quasicircles. We characterize the Dirichlet space of $\Sigma$ as an isomorphic image of a direct sum of Dirichlet spaces of the disk under a…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain $\Omega \subset \mathbb{R}^{d},$ where $d = 2, 3$, in…