We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.

We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.

We introduce an intrinsic notion of Hölder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of Littlewood-Paley decomposition in characterizing Hölder-Zygmund regularity for distributions. It is based on a simple interplay of different...

We introduce an intrinsic notion of Zygmund regularity for Colombeau algebras of generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of the wavelet transform as a tool in studying Hölder-Zygmund regularity. It is based on a simple mollifier-wavelet interplay which transl...

In this work, we give several characterizations of the bounded and the compact weighted composition operators from the Lipschitz space into the Zygmund space. Mathematics subject classification (2010): Primary 47B33; secondary 30H05.

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

After the pioneer work of Calderón and Zygmund in the 50’s, the systematic study of singular integrals has become a corner stone in harmonic analysis with deep implications in mathematical physics, partial differential equations and other mathematical disciplines. Subsequent generalizations of Calderón-Zygmund theory have essentially pursued two lines. We may either consider more general domain...

We introduce an intrinsic notion of Zygmund regularity for Colombeau algebras of generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of the wavelet transform as a tool in studying Hölder regularity. It is based on a simple mollifier-wavelet interplay which translates wav...

The Beppo-Levi native spaces which arise when using polyharmonic splines to interpolate in many space dimensions are embedded in Hölder-Zygmund spaces. Convergence rates for radial basis function interpolation are inferred in some special cases.