The Shearlet Transform and Lizorkin Spaces

• Autores: Francesco Bartolucci, Stevan Pilipovic, Nenad Teofanov
• Localización: Landscapes of Time-Frequency Analysis: ATFA 2019 / coord. por Paolo Boggiatto, 2020, ISBN 978-3-030-56005-8, págs. 43-62
• Idioma: inglés
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• Resumen

  • We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here the shearlet synthesis operator, and we prove its continuity on the space of smooth and rapidly decreasing functions over R2 × R × R×. Then, we use these continuity results to extend the shearlet transform to the space of Lizorkin distributions via the duality approach, and we prove its consistency with the classical definition for test functions and its equivalence with the coorbit space approach.