Sparse technology in weighted harmonic analysis
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This dissertation is the union of two major results that we discovered during my graduate time. Both of the results involve what are called sparse families of cubes. There will also be some partial results included though they were not submitted to any peer-reviewed journal. In this work, we first provide an example that directly disproves the Muckenhoupt-Wheeden conjectures for sparse operators. More specifically, we will construct a pair of weights