Center for Research and Development in Mathematics and Applications

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On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators

Publication . Alabalik, Aysegul C.; Almeida, Alexandre; Samko, Stefan

We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C-0(infinity) (R-n) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy-Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.

2020-07Journal article

Open access

Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators

Publication . Alabalik, Aysegul C.; Almeida, Alexandre; Samko, Stefan

We show that certain vanishing properties defining closed subspaces of generalized Morrey spaces are preserved under the action of various classical operators of harmonic analysis, such as maximal operators, singular-type operators, Hardy operators, and fractional integral operators. Those vanishing subspaces were recently used to deal with the delicate problem on the description of the closure of nice functions in Morrey norm.

2020-11Journal article

Restricted access

Bounding anisotropic Lorentz invariance violation from measurements of the effective energy scale of quantum gravity

Publication . Guerrero, Merce; Campoy-Ordaz, Anna; Potting, Robertus; Gaug, Markus

Observations of energy-dependent photon time delays from distant flaring sources provide significant constraints on Lorentz invariance violation (LIV). Such effects originate from modified vacuum dispersion relations causing differences in propagation times for photons emitted simultaneously from gamma-ray bursts, active galactic nuclei, or pulsars. These modifications are often parametrized within a general framework by an effective quantum gravity energy scale EQG;n. While such general constraints are well established in the LIV literature, their translation into specific coefficients of alternative theoretical frameworks, such as the Standard-Model extension (SME), is rarely carried out. In particular, existing bounds on the quadratic case (n ¼ 2) of EQG;n can be systematically converted into constraints on the nonbirefringent, CPT-conserving SME coefficients c ð6Þ ðIÞjm. This work provides a concise overview of the relevant SME formalism and introduces a transparent conversion method from EQG;2 to SME parameters. We review the most stringent time-of-flight-based bounds on EQG;n and standardize them by accounting for systematics, applying missing prefactors, and transforming results into two-sided Gaussian uncertainties where needed. We then use these standardized constraints, along with additional bounds from the literature, to improve bounds on the individual SME coefficients of the photon sector by about an order of magnitude. A consistent methodology is developed to perform this conversion from the general LIV framework to the SME formalism.

2025-11-04Journal article

Open access