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HARDY TYPE INEQUALITIES FOR THE FRACTIONAL RELATIVISTIC OPERATOR

(2022-01-01)

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Cp ESTIMATES FOR ROUGH HOMOGENEOUS SINGULAR INTEGRALS AND SPARSE FORMS

Canto, J.; Li, K.; Roncal, L.; Tapiola, O. (2021-01-01)

We consider Coifman–Fefferman inequalities for rough homogeneous singular integrals TΩ and Cp weights. It was recently shown in [33] that ∥TΩ∥Lp(w) ≤ Cp,T,w∥Mf∥Lp(w) for every 0 < p < ∞ and every w ∈ A∞. Our first goal is ...

ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN

Fernández-Bertolin, A.; Roncal, L.; Rüland, A. (2023-01-01)

We study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (g...

MAXIMAL OPERATORS ON THE INFINITE-DIMENSIONAL TORUS

Kosz, D.; Martinez-Perales, J.C.; Paternostro, V.; Rela, E.; Roncal, L. (2022-01-01)

We study maximal operators related to bases on the infinite- dimensional torus Tω. For the normalized Haar measure dx on Tω it is known that MR0, the maximal operator associated with the dyadic basis R0, is of weak type (1,1...