Book (by default) and report (with openright class
option) ensure that each chapter starts on a right-hand (recto) page;
they do this by inserting a \cleardoublepage command between
chapters (rather than a mere \clearpage). The empty page thus
created gets to have a normal running header, which some people don't
like.
The (excellent) fancyhdr manual covers this issue, basically
advising the creation of a command \clearemptydoublepage:
\let\origdoublepage\cleardoublepage
\newcommand{\clearemptydoublepage}{%
\clearpage
{\pagestyle{empty}\origdoublepage}%
}
The "obvious" thing is then to use this command to replace
\cleardoublepage in a patched version of the \chapter command.
(Make a package of your own containing a copy
of the command out of the class.) This isn't particularly difficult,
but you can instead simply subvert \cleardoublepage (which isn't
often used elsewhere):
\let\cleardoublepage\clearemptydoublepageNote: this command works because
\clearemptydoublepage uses a copy
of \cleardoublepage: instructions on macro programming
patching techniques explain the problem and
why this is a solution.
Note that the KOMA-Script replacements for the
book amd report classes (scrbook and
scrreprt offers class options cleardoubleempty,
cleardoubleplain and cleardoublestandard
(using the running page style, as normal) that control the appearance
of these empty pages. The classes also offer do-it-yourself commands
\cleardoubleempty (etc.). The memoir class
provides commands \cleartooddpage and \cleartoevenpage,
which both take an optional argument (the first, with no argument,
being an equivalent of \cleardoublepage). One can achieve
'special' effects by putting commands in the optional argument: the
\clearemptydoublepage we're after would be achieved by
\cleartooddpage[\thispagestyle{empty}].
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