Harmonic Analysis
http://hdl.handle.net/20.500.11824/3
2023-10-19T08:24:38ZWeighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
http://hdl.handle.net/20.500.11824/1691
Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
Nieraeth, Z.; Rey, G.
In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces.
2023-05-01T00:00:00ZWeighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
http://hdl.handle.net/20.500.11824/1689
Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
Accomazzo, N.; Duoandikoetxea, J.; Nieraeth, Z.; Ombrosi, S.; Pérez, C.
We prove the sharp mixed Ap−A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free and can also be used to bound similar operators, even in the two-weight setting. We use this to also obtain new quantitative bounds for the strong maximal operator and for M in a dual setting.
2023-03-15T00:00:00ZExtrapolation in general quasi-Banach function spaces
http://hdl.handle.net/20.500.11824/1688
Extrapolation in general quasi-Banach function spaces
Nieraeth, Z.
In this work we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization of the Hardy-Littlewood maximal operator to very general bases that includes a method to obtain self-improvement results that are sharp with respect to its operator norm. Furthermore, we prove bounds for the Hardy-Littlewood maximal operator in weighted Lorentz, variable Lebesgue, and Morrey spaces, and recover and extend several extrapolation theorems in the literature. Finally, we provide an application of our results to the Riesz potential and the Bilinear Hilbert transform.
2023-11-15T00:00:00ZOn C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
http://hdl.handle.net/20.500.11824/1638
On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining
Ponce Vanegas, F.; Bizzarri, M.; Barton, M.
We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2,
the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.
2023-10-01T00:00:00Z