Currently displaying 1 – 14 of 14

Showing per page

Order by Relevance | Title | Year of publication

H p spaces associated with Schrödinger operators with potentials from reverse Hölder classes

Jacek DziubańskiJacek Zienkiewicz — 2003

Colloquium Mathematicae

Let A = -Δ + V be a Schrödinger operator on d , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of H A p if the maximal function s u p t > 0 | T t f ( x ) | belongs to L p ( d ) , where T t t > 0 is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space H A p admits a special atomic decomposition.

Hardy space H associated to Schrödinger operator with potential satisfying reverse Hölder inequality.

Jacek DziubanskiJacek Zienkiewicz — 1999

Revista Matemática Iberoamericana

Let {T} be the semigroup of linear operators generated by a Schrödinger operator -A = Δ - V, where V is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space H by means of a maximal function associated with the semigroup {T}. Atomic and Riesz transforms characterizations of H are shown.

Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Jacek DziubańskiWaldemar HebischJacek Zienkiewicz — 1994

Studia Mathematica

Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let p t be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that | p 1 ( x ) | C e x p ( - c τ ( x ) d / ( d - 1 ) ) . Moreover, if G is not stratified, more precise estimates of p 1 at infinity are given.

Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa DamekJacek DziubańskiAndrzej HulanickiJose L. Torrea — 2002

Colloquium Mathematicae

Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.

Functional calculus in weighted group algebras.

Jacek DziubanskiJean LudwigCarine Molitor-Braun — 2004

Revista Matemática Complutense

Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L(G,ω). This functional calculus is then used to study harmonic analysis properties of L(G,ω), such as the Wiener property and Domar's theorem.

Page 1

Download Results (CSV)