BOUNDEDNESS OF GENERALIZED RIESZ POTENTIALS ON THE VARIABLE HARDY SPACES

Generalized Bessel and Riesz Potentials on Metric Measure Spaces

There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study of various current topics, such as the ...

On the (p,q)-Boundedness of Nonisotropic Spherical Riesz Potentials

On the Generalized Hardy Spaces

and Applied Analysis 3 Definition 2.1. Let F : H U → H U be a linear operator such that F f 0 if and only if f 0, that is, F is 1-1. For 1 ≤ p < ∞, the generalized Hardy space HF,p U HF,p is defined to be the collection of all analytic functions f on U for which

Boundedness of the Riesz Projection on Spaces with Weights

Let ∂D be the unit circle in the complex plane, define the function χ on ∂D by χ(eiθ) = eiθ, and set P = {p : p = ∑Nk=−N ckχ}. Let σ be normalized Lebesgue measure on ∂D. The Riesz projection P+ is defined on P by the formula P+( ∑N k=−N ckχ k) = ∑N k=0 ckχ k. In [4], Paul Koosis proved: Theorem 1 (Koosis). Given a non-negative function w ∈ L1, there exists a non-negative, non-trivial function ...

On Continuity of Generalized Riesz Potentials

This study establishes the theorem on continuity of generalized Riesz potentials with non-isotropic kernels depending on (β, γ)-distance. Mathematics Subject Classification: 31B10, 42B20, 47B06