Real Hardy spaces on real rank 1 semisimple Lie groups

Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One

Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will prove that L(G) ∗ L(G) ⊆ L(G), which is a sharp endpoint estimate for the Kunze-Stein phenomenon. We will also show that the noncentered maximal operator M2f(z) = sup z∈B 1 |B| ∫ B f(z)dz is bounded from ...

Harmonic Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One

Let G be a real semisimple Lie group. Harish-Chandra has defined the Schwartz space, V[G), on G. A tempered distribution on G is a continuous linear functional on R G ) . If the real rank of G equals one, Harish-Chandra has published a version of the Plancherel formula for I^(G) [3(k), 5241. We restrict the Fourier transform map to %(G), and we compute the image of the space V(G) [Theorem 31. T...

Equivariant derived category and representation of real semisimple Lie groups

Realizations of real semisimple low-dimensional Lie algebras Realizations of real semisimple low-dimensional Lie algebras

A complete set of inequivalent realizations of threeand four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained. Representations of Lie algebras by vector fields are widely applicable e.g. in integrating of ordinary differential equations, group classification of partial differential equations, the theory of differential...

Cauchy–Szegö kernels for Hardy spaces on simple Lie groups

For any simple real group G possessing unitary highest weight representations one can define the Hardy space H(G) . This is a Hilbert space formed by holomorphic functions in a ‘non–commutative’ tube domain Γ satisfying a Hardy–type condition (Γ is the interior of a non– commutative complex semigroup Γ containing the group G ). The space H(G) is identified with the bi–invariant subspace of L(G)...