David Beltran, Universitat de Valencia, Burjassot, Spain, Joris Roos, University of Massachusetts Lowell, Massachusetts, and Andreas Seeger, University of Wisconsin-Madison, Wisconsin.

• 1. Introduction2. Necessary Conditions3. Single scale sparse domination4. Proof of the main result5. Maximal operators, square functions and long variations6. Fourier multipliers7. Sample applicationsA. Facts about sparse dominationB. Sparse domination: Cases where $p=1$ or $q=\infty $C. Facts about fourier multipliers

David Beltran, Universitat de Valencia, Burjassot, Spain, Joris Roos, University of Massachusetts Lowell, Massachusetts, and Andreas Seeger, University of Wisconsin-Madison, Wisconsin.

• 1. Introduction2. Necessary Conditions3. Single scale sparse domination4. Proof of the main result5. Maximal operators, square functions and long variations6. Fourier multipliers7. Sample applicationsA. Facts about sparse dominationB. Sparse domination: Cases where $p=1$ or $q=\infty $C. Facts about fourier multipliers

David Beltran, Universitat de Valencia, Burjassot, Spain, Joris Roos, University of Massachusetts Lowell, Massachusetts, and Andreas Seeger, University of Wisconsin-Madison, Wisconsin.

• 1. Introduction2. Necessary Conditions3. Single scale sparse domination4. Proof of the main result5. Maximal operators, square functions and long variations6. Fourier multipliers7. Sample applicationsA. Facts about sparse dominationB. Sparse domination: Cases where $p=1$ or $q=\infty $C. Facts about fourier multipliers