Monthly Archives: March 2011

DMat0101, Notes 5: The Hardy-Littlewood maximal function

1. Averages and maximal operators This week we will be discussing the Hardy-Littlewood maximal function and some closely related maximal type operators. In order to have something concrete let us first of all define the averages of a locally integrable … Continue reading

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DMat0101, Notes 4: The Fourier transform of the Schwartz class and tempered distributions

In this section we go back to the space of Schwartz functions and we define the Fourier transform in this set up. This will turn out to be extremely useful and flexible. The reason for this is the fact that … Continue reading

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DMat0101, Notes 3: The Fourier transform on L^1

1. Definition and main properties. For , the Fourier transform of is the function Here denotes the inner product of and : Observe that this inner product in is compatible with the Euclidean norm since . It is easy to … Continue reading

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