Linear transforms and convolution
Linearization and Connection Coefficients of Orthogonal Polynomials.
Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization...
Linearly-invariant families and generalized Meixner–Pollaczek polynomials
The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f′(z)) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f′0(z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials Pλn (x; θ,ψ) of a real variable x as coefficients of [###] where the parameters...
Lions-Peetre reiteration formulas for triples and their applications
We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted -spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability...
Lipschitz and bi-Lipschitz functions.
Lipschitz Classes and Restrictions of Fourier Transforms.
Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces
We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
Lipschitz estimates for multilinear commutator of Litllewood-Paley operator
Lipschitz estimates for multilinear commutator of Littlewood-Paley operator.
Lipschitz estimates for multilinear commutator of pseudo-differential operators.
Lipschitz measures and vector-valued Hardy spaces.
Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.
In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of...
Lipschitz Spaces on Compact Lie Groups.
Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space
Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups
We give a characterization of the Hölder-Zygmund spaces () on a stratified Lie group in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on , in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces...
Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
Let be a closed null set. We prove an equivalence between the Littlewood-Paley decomposition in with respect to the complementary intervals of and Fourier multipliers of Hörmander-Mihlin and Marcinkiewicz type with singularities on . Similar properties are studied in for a union of rays from the origin. Then there are connections with the maximal function operator with respect to all rectangles parallel to these rays. In particular, this maximal operator is proved to be bounded on , ,...
Littlewood-Paley decompositions on manifolds with ends
For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) spaces, using the usual square function defined by a dyadic partition.
Littlewood-Paley -function in the Dunkl analysis on .
Littlewood-Paley g-functions with rough kernels on homogeneous groups
Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾