• Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces 

  Nieraeth, Z.; Rey, G. (2023-05-01)

  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.

• 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. (2023-03-15)

  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 ...

• Extrapolation in general quasi-Banach function spaces 

  Nieraeth, Z. (2023-11-15)

  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 ...

• 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. (2023-10)

  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, ...

• Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres 

  Iosevich, A.; Langowski, B.; Mirek, M.; Szarek, T.Z. (2023-01-01)

  We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ...

• On the advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity 

  Bonicatto, P.; Ciampa, G.; Crippa, G. (2022-11-01)

  We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergence-free vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ...

• Self-improving Poincaré-Sobolev type functionals in product spaces 

  Cejas, M.E.; Mosquera, C.; Pérez, C.; Rela, E. (2021)

  In this paper we give a geometric condition which ensures that (q, p)-Poincar´e-Sobolev inequalities are implied from generalized (1, 1)-Poincar´e inequalities related to L 1 norms in the context of product spaces. ...

• Cones with convoluted geometry that always scatter or radiate 

  Blåsten, E.L.K.; Pohjola, V. (2021)

  We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be an arbitrary non-trivial Herglotz wave. We show that a large number of such local conical scatterers ...

• The Hajłasz capacity density condition is self-improving 

  Canto, J.; Vähäkangas, A.V. (2021)

  We prove a self-improvement property of a capacity density condition for a nonlocal Haj lasz gradient in complete geodesic spaces. The proof relates the capacity density condition with boundary Poincar´e inequalities, ...

• On quantitative Runge approximation for the time harmonic Maxwell equations. 

  Pohola, V. (2021)

  Here we derive some results on so called quantitative Runge approximation in the case of the time-harmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally ...

• Sawyer-type inequalities for Lorentz spaces 

  Pérez, C.; Roure-Perdices, E. (2022-06)

  The Hardy-Littlewood maximal operator M satisfies the classical Sawyer-type estimate ∥Mfv∥L1,∞(uv)≤Cu,v‖f‖L1(u),where u∈ A1 and uv∈ A∞. We prove a novel extension of this result to the general restricted weak type case. ...

• Notes on $H^{\log}$: structural properties, dyadic variants, and bilinear $H^1$-$BMO$ mappings 

  Bakas, O.; Pott, S.; Rodríguez-López, S.; Sola, A. (2022)

  This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy ...

• Polynomial averages and pointwise ergodic theorems on nilpotent groups 

  Ionescu, A. D.; Magyar, A.; Mirek, M.; Szarek, T.Z. (2022)

  We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on $\sigma$-finite measure spaces. We also establish ...

• Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group 

  Fanelli, L.; Roncal, L. (2022-11-04)

  We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood--Paley ...

• A∞ condition for general bases revisited: complete classification of definitions 

  Kosz, D. (2022-05-27)

  We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ...

• Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups 

  Roncal, L.; Thangavelu, S. (2021-03-10)

  Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238--4294. They concern ...

• Maximal operators on the infinite-dimensional torus 

  Roncal, Luz; Kosz, D.; Martínez-Perales, J.; Paternostro, V.; Rela, E.; Roncal, L. (2022-03-31)

  We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ...

• The Frisch–Parisi formalism for fluctuations of the Schrödinger equation 

  Kumar, S.; Ponce Vanegas, F.; Roncal, L.; Vega, L. (2022)

  We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ...

• Rotational smoothing 

  Caro, P.; Meroño, C.; Parissis, I. (2022-01-05)

  Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators ...

• Geometric Harmonic Analysis 

  Canto, J. (2021)

  This thesis is the compilation of the results obtained during my PhD, which started in January 2018 and is being completed in the end of 2021. The main matter is divided into  ve chapters, Chapters 2 6. Each of these ...

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