Osane Oruetxebarria | University of the Basque Country, Euskal Herriko Unibertsitatea (original) (raw)

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Papers by Osane Oruetxebarria

Research paper thumbnail of Mixed Norm Estimates for Potential Operators Related to the Radon Transform

Journal of The Australian Mathematical Society, Apr 1, 2008

Research paper thumbnail of Estimates for radial solutions to the wave equation

Proceedings of the American Mathematical Society, Dec 21, 2015

Research paper thumbnail of Weighted mixed‐norm inequalities through extrapolation

Mathematische Nachrichten, Feb 28, 2019

Research paper thumbnail of The spherical maximal operator on radial functions

Journal of Mathematical Analysis and Applications, Mar 1, 2012

Research paper thumbnail of K-Plane Transforms and Related Operators on Radial Functions

Michigan Mathematical Journal, Oct 1, 2001

Research paper thumbnail of Interdisciplinary Training Assessment of Communication Skills for Students with Basque as Instruction Language in the Faculty of Science and Technology at Upv/Ehu University

EDULEARN18 Proceedings, Jul 1, 2018

Research paper thumbnail of Weighted mixed‐norm inequalities through extrapolation

Mathematische Nachrichten, 2019

We prove that operators satistying weighted inequalities with radial weights are bounded in mixed... more We prove that operators satistying weighted inequalities with radial weights are bounded in mixed‐norm spaces of radial‐angular type, even with a weight in the radial part. This is achieved by using the usual extrapolation methods, adapted to the radial setting. All the versions of the extrapolation theorem can be adapted to this setting, and in particular we get results in variable Lebesgue spaces and also for multilinear operators. Furthermore, quantitative estimates are obtained with this approach, but their sharpness remains an open question.

Research paper thumbnail of Estimates for radial solutions to the wave equation

Proceedings of the American Mathematical Society, 2015

Research paper thumbnail of Radial Ap wights with aplications to the disc multiplier and the Bochner-Riesz operators

Indiana University Mathematics Journal

Research paper thumbnail of Mixed Norm Inequalities for Directional Operators Associated to Potentials

Potential Analysis

We study mixed norm inequalities for directional operators which appear applying the method of ro... more We study mixed norm inequalities for directional operators which appear applying the method of rotations to homogeneous operators with variable kernel and with the homogeneity of Riesz potentials. The results are sharp for a range of values of the parameter and for all its values when the inequalities are restricted to radial functions.

Research paper thumbnail of Mixed Norm Estimates for Potential Operators Related to the Radon Transform

Journal of the Australian Mathematical Society, 2008

We define potential operators on hyperplanes and give sharp mixed norm inequalities for them. One... more We define potential operators on hyperplanes and give sharp mixed norm inequalities for them. One of the operators coincides with the Radon transform for which mixed norm estimates are known but in reverse order. Those inequalities will be crucial in our proofs.

Research paper thumbnail of The spherical maximal operator on radial functions

Journal of Mathematical Analysis and Applications, 2012

We use simple one-dimensional operators to bound pointwise the spherical maximal operator acting ... more We use simple one-dimensional operators to bound pointwise the spherical maximal operator acting on radial functions. With this bounds we obtain weighted inequalities, which are sharp for power weights. We also discuss boundedness results on Morrey spaces and give a Fefferman-Stein type inequality. The bounds of the two-dimensional case can be use for the universal maximal operator as well.

Research paper thumbnail of Radial <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">A_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> weights with applications to the disc multiplier and the Bochner-Riesz operators

Indiana University Mathematics Journal, 2008

A characterization of radial A p weights is given in terms of the weights in A p (0, +∞). Togethe... more A characterization of radial A p weights is given in terms of the weights in A p (0, +∞). Together with a result of Mockenhaupt this allows to describe a large class of radial weights for the disc multiplier in terms of the A 2 class of Muckenhoupt. The class of weights is large enough so as to deduce mixed norm inequalities with weights in the radial direction using extrapolation. Similar results are obtained for the Bochner-Riesz operators and for the Littlewood-Paley square function built on characteristic functions of dyadic annuli.

Research paper thumbnail of K-Plane Transforms and Related Operators on Radial Functions

Michigan Mathematical Journal, 2001

Research paper thumbnail of Matematika eta Euskal Dantzak

Mathematics and dance may be thought as disciplines very far away one from each other and it may ... more Mathematics and dance may be thought as disciplines very far away one from each other and it may seem that finding links between them is impossible, but in this paper we will show that this is not true. Wearing mathematical glasses, we will easily find basic geometrical concepts. On one hand, we will see that dancers, when organized in groups, form circumferences, rectangles and other polygons; on the other hand, we will describe symmetries among dancers’ positions, by means of rotations, translations and reflections. We will also describe other dances making use of deeper and less obvious concepts, such as permutations and combinations from combinatorics and braid theory from topology.

Research paper thumbnail of Mixed Norm Estimates for Potential Operators Related to the Radon Transform

Journal of The Australian Mathematical Society, Apr 1, 2008

Research paper thumbnail of Estimates for radial solutions to the wave equation

Proceedings of the American Mathematical Society, Dec 21, 2015

Research paper thumbnail of Weighted mixed‐norm inequalities through extrapolation

Mathematische Nachrichten, Feb 28, 2019

Research paper thumbnail of The spherical maximal operator on radial functions

Journal of Mathematical Analysis and Applications, Mar 1, 2012

Research paper thumbnail of K-Plane Transforms and Related Operators on Radial Functions

Michigan Mathematical Journal, Oct 1, 2001

Research paper thumbnail of Interdisciplinary Training Assessment of Communication Skills for Students with Basque as Instruction Language in the Faculty of Science and Technology at Upv/Ehu University

EDULEARN18 Proceedings, Jul 1, 2018

Research paper thumbnail of Weighted mixed‐norm inequalities through extrapolation

Mathematische Nachrichten, 2019

We prove that operators satistying weighted inequalities with radial weights are bounded in mixed... more We prove that operators satistying weighted inequalities with radial weights are bounded in mixed‐norm spaces of radial‐angular type, even with a weight in the radial part. This is achieved by using the usual extrapolation methods, adapted to the radial setting. All the versions of the extrapolation theorem can be adapted to this setting, and in particular we get results in variable Lebesgue spaces and also for multilinear operators. Furthermore, quantitative estimates are obtained with this approach, but their sharpness remains an open question.

Research paper thumbnail of Estimates for radial solutions to the wave equation

Proceedings of the American Mathematical Society, 2015

Research paper thumbnail of Radial Ap wights with aplications to the disc multiplier and the Bochner-Riesz operators

Indiana University Mathematics Journal

Research paper thumbnail of Mixed Norm Inequalities for Directional Operators Associated to Potentials

Potential Analysis

We study mixed norm inequalities for directional operators which appear applying the method of ro... more We study mixed norm inequalities for directional operators which appear applying the method of rotations to homogeneous operators with variable kernel and with the homogeneity of Riesz potentials. The results are sharp for a range of values of the parameter and for all its values when the inequalities are restricted to radial functions.

Research paper thumbnail of Mixed Norm Estimates for Potential Operators Related to the Radon Transform

Journal of the Australian Mathematical Society, 2008

We define potential operators on hyperplanes and give sharp mixed norm inequalities for them. One... more We define potential operators on hyperplanes and give sharp mixed norm inequalities for them. One of the operators coincides with the Radon transform for which mixed norm estimates are known but in reverse order. Those inequalities will be crucial in our proofs.

Research paper thumbnail of The spherical maximal operator on radial functions

Journal of Mathematical Analysis and Applications, 2012

We use simple one-dimensional operators to bound pointwise the spherical maximal operator acting ... more We use simple one-dimensional operators to bound pointwise the spherical maximal operator acting on radial functions. With this bounds we obtain weighted inequalities, which are sharp for power weights. We also discuss boundedness results on Morrey spaces and give a Fefferman-Stein type inequality. The bounds of the two-dimensional case can be use for the universal maximal operator as well.

Research paper thumbnail of Radial <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">A_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> weights with applications to the disc multiplier and the Bochner-Riesz operators

Indiana University Mathematics Journal, 2008

A characterization of radial A p weights is given in terms of the weights in A p (0, +∞). Togethe... more A characterization of radial A p weights is given in terms of the weights in A p (0, +∞). Together with a result of Mockenhaupt this allows to describe a large class of radial weights for the disc multiplier in terms of the A 2 class of Muckenhoupt. The class of weights is large enough so as to deduce mixed norm inequalities with weights in the radial direction using extrapolation. Similar results are obtained for the Bochner-Riesz operators and for the Littlewood-Paley square function built on characteristic functions of dyadic annuli.

Research paper thumbnail of K-Plane Transforms and Related Operators on Radial Functions

Michigan Mathematical Journal, 2001

Research paper thumbnail of Matematika eta Euskal Dantzak

Mathematics and dance may be thought as disciplines very far away one from each other and it may ... more Mathematics and dance may be thought as disciplines very far away one from each other and it may seem that finding links between them is impossible, but in this paper we will show that this is not true. Wearing mathematical glasses, we will easily find basic geometrical concepts. On one hand, we will see that dancers, when organized in groups, form circumferences, rectangles and other polygons; on the other hand, we will describe symmetries among dancers’ positions, by means of rotations, translations and reflections. We will also describe other dances making use of deeper and less obvious concepts, such as permutations and combinations from combinatorics and braid theory from topology.